Would you like the short answer on the long answer?

The short answer if that 4 fairly attractive men could make music good together and people were attracted to them because of that.

The long answer is that Lennon/McCartney spent more time studying what made a song popular, or catchy, or relevant than any musician ever has, for or since.

They tried to write in different styles, and especially once they'd already been successful, they experimented, but realistically, for the most part, they always tried to innovate on what had already been successful- take something good and make it better.

But most of the innovation happened later, once Beatle-Mania was already firmly entrenched, and regardless of the styles the wrote in.

So, I guess the real answer (long or short) is that the first boy band ever happened to all be geniuses who knew their history an tried to emulate it as well as their contemporaries...and did it well. and also, their looks didn't hurt.