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In an interview I read, a 747 captain (Mark Vanhoenacker, an American British Airways pilot) says he doesn't understand why he cannot listen to music inflight, when for example surgeons – who literally hold peoples' lives in their hands – can:

Can you ever play music in the cockpit?
Sadly no. Sometimes when your flight is delayed, on the ground waiting
for a couple hours, without passengers on board, you might put some
music on in the cockpit. On the radio, you might hear a little music
break through on an air traffic control frequency, those frequencies
aren't much higher than the ones used by commercial radio stations.
But as for listening to music while flying, no—which I don't
understand! I think surgeons can listen to Beethoven if they want,
right?

I looked that up and sure enough, some surgeons really listen to music and it even improves their performance:

"From classical to rock, music can be heard in operating rooms across
the world. When plastic surgeons listen to music they prefer, their
surgical technique and efficiency when closing incisions is improved,
a new study shows."

So why is it not allowed for airline pilots ?

I don't know where he gets that. Regulation wise there's nothing stopping an airline pilot from listening to music as long as he/she can hear ambient sounds or communications and modern headsets make it easy to link an ipod to headphones that are also receiving the comms.

Pilots are allowed to take naps in flight as long as they are awake within 45 min of arrival. A pilot not flying (PNF), where the autopilot is on and the other pilot is monitoring everything, can be doing paperwork or reading a paper or watching a movie on a tablet or going for a dump or wandering around the cabin if he/she wants. Once on an arrival however, forget it and certainly not once below 10000 ft.

If there is a prohibition in that Capt's case, it is probably a policy with that airline.

This is likely to be a subject where the answer varies by jurisdiction.

In the USA, there are some limits for pilots flying commercial airliners in scheduled airline passenger service (i.e. Part 121 operations.) In particular, most of the types of devices that would be used to play said music are banned for use by pilots during all phases of flight in Part 121 operations.

14 CFR 121.542(d) says the following:

(d) During all flight time as defined in 14 CFR 1.1, no flight crewmember may use, nor may any pilot in command permit the use of, a personal wireless communications device (as defined in 49 U.S.C. 44732(d)) or laptop computer while at a flight crewmember duty station unless the purpose is directly related to operation of the aircraft, or for emergency, safety-related, or employment-related communications, in accordance with air carrier procedures approved by the Administrator.

49 U.S.C. 44732(d) defines "personal wireless communications device" as:

(d) Personal Wireless Communications Device Defined.—

In this section, the term “personal wireless communications device” means a device through which personal wireless services (as defined in section 332(c)(7)(C)(i) of the Communications Act of 1934 (47 U.S.C. 332(c)(7)(C)(i))) are transmitted.

This particular question of being able to play music came up when this regulation was added back in 2014. The FAA had this to say about it in their final rule publication in the Federal Register (emphasis mine):

PROHIBITED DEVICES

Several commenters asked if the limitations in the rule extended to specific devices, such as iPods, used to listen to music. As stated in the NPRM, Section 307 of the Act defines “personal wireless communications device” as a device through which personal wireless services (as defined in Section 332(c)(7)(C)(i) of the Communications Act of 1934) are transmitted.[5] The Communications Act of 1934 states that personal wireless services means commercial mobile services, unlicensed wireless services, and common carrier wireless exchange access service.

In general, wireless telecommunications is the transfer of information between two or more points that are not physically connected. In the final rule, the FAA retains the same broad category of included devices because a list of specific devices would ignore the reality of evolving technology. This broad category includes, but is not limited to, devices such as cell phones, smartphones, personal digital assistants, tablets, e-readers, some (but not all) gaming systems, iPods and MP3 players, as well as netbooks and notebook computers.

Evolving technology makes it difficult to develop an inclusive list of devices that are addressed by the provisions of the final rule. The FAA notes that the final rule establishes a clear definition of personal wireless communications devices. The provisions of the final rule do not prohibit the use of devices that do not meet the definition of personal wireless communications devices.

So, while playing music isn't specifically banned, most of the devices that would be used to do so are in Part 121 operations. Part 121 operations are those operated by U.S.-flagged scheduled air carriers. It does appear that a Part 121 pilot could still play music (during non-critical flight phases) using an MP3 player that had no wireless communications functionality (i.e. no Wi-Fi, Bluetooth, or cellular radio.)

As far as the 'why' part of the question, this is also addressed by the final rule publication in the Federal Register:

B. Statement of the Problem

Several incidents involving a breakdown of cockpit discipline prompted Congress to address this issue via legislation. In one instance, two pilots were using their personal laptop computers during cruise flight and lost situational awareness, leading to a 150 mile fly-by of their destination. In another instance, a pilot sent a text message on her personal cell phone during the taxi phase of the flight after the aircraft pushed back from the gate and before the take-off sequence. These incidents illustrate the potential for such devices to create a hazardous distraction during critical phases of flight.

This rule will ensure that certain non-essential activities do not contribute to the challenge of task management on the flight deck and do not contribute to a loss of situational awareness due to attention to non-essential activities, as highlighted by these incidents. See 78 FR 2912 (Jan. 15, 2013).

C. National Transportation Safety Board Recommendations

In its recommendations to the FAA regarding the Colgan accident in 2009, the National Transportation Safety Board (NTSB) concluded that because of the continuing number of accidents involving a breakdown in sterile cockpit discipline, collaborative action by the FAA and the aviation industry to address this issue was warranted. Therefore, the NTSB recommended (A-10-30) that the FAA require all part 121, 135, and 91 subpart K operators to incorporate explicit guidance to pilots, including checklist reminders as appropriate, prohibiting the use of personal portable electronic devices on the flight deck.

The document then goes on to describe another incident that motivated the NTSB recommendation where a medevac helicopter crashed killing the pilot, nurse, paramedic, and patient. The helicopter's engine failed due to fuel exhaustion due to the pilot not ensuring that the helicopter was adequately fueled prior to departure. "The investigation determined that the pilot engaged in frequent personal texting, both before and during the accident flight."

So, in short, all use of personal wireless communications devices in Part 121 operations was banned due in order to prevent dangerous crew distraction from texting and such.

I couldn't comment on this post here, but check this out:
Is it allowed to listen to music while piloting a plane?

Not exactly sure where you heard from this 747 pilot but I'm pretty sure it's allowed by the FAA. If it's not allowed for that specific pilot it may be from company policies.

Just some ideas though, maybe the music could be distracting to the pilot?

In an interview I read, a 747 captain....

You refer to him as a captain. However, in the article's image, he's sitting in the first officer's seat and is wearing three stripes, so it would appear that he's not a captain.

... why he cannot listen to music inflight, when for example surgeons – who literally hold peoples' lives in their hands – can....

A surgeon's functioning model is markedly different from that of a pilot in cruising flight. The surgeon is actively doing something causing moment by moment changes in front of him, which he observes visually and to some degree by feel, but typically not by sound. The pilot is monitoring, not causing changes, and his monitoring needs to be cognizant of changes in sound. And, of course, if the surgeon screws up, he only kills one person. A 747 captain can kill 480 at a time...plus maybe some on the ground.

Here's an example that applies to both the 747-100 and -200 aircraft. It possibly applies to the -400 too, but I never flew them. Let's say you're in cruise at night—can't see a thing out the windshield—and a fairly high frequency sound starts, building slowly but getting louder. Who is more likely to first notice that, a pilot listening to music or one who is not, and why does it matter?

Likely the music guy is not going to notice it first, but I'm guessing he will hear the loud cracking sound that can eventually occur. What's happening is that you're icing badly. The ice is collecting on a windshield wiper such that it's starting to vibrate, and it can finally break off—the wiper, not the ice, happened to me once— and you need to do something (change altitude?), not just because of the wiper, but because it's not a good idea to stay in icing any longer than you have to.

Now that's a bit of an unusual example, but, really, you need to be attuned to the sounds of the airplane. Let's say you're in oceanic control and for some reason you're monitoring the HF and start hearing small but sharp crackles. Best start looking around for lightning, check the radar, etc. There are lots of reasons to not impede your ability to hear things.

Neither of the two 747 carriers I flew for specifically prohibited it. However, I wouldn't have allowed it when I was a captain, and with possibly one exception I don't think any of the captains I flew with as a first officer would have allowed it.

Yes, ear buds, etc are banned on buses and 18 wheelers for drivers. If there's something going wrong with the engine or vehicle you cannot hear it. Hearing something critical going wrong early would mean lives saved.

Update: School Bus drivers are not allowed any music what so ever, but if a passenger on any type of bus plays music of their own it is not against any policies.