They are wrong, it's a wonderful time to have a baby! DC1 was born on 25th December. DH always says, best Christmas gift he'll ever get!
For their actual birthday, you are already all together on Christmas Day. As we always have birthday cake and candles, I never again have to make a fucking awful christmas cake (hate fruit cake).
Because their birthday is actually at Christmas, you can justify having a party in July and second round of gifts then to spread it out, but if they say, have an end of November birthday, it's far enough away that you can't really push their party/gift buying to another time of year, and IME, people with November and January birthdays don't get as much stuff and fuss anyway because of the cost/planning of Christmas. (November and January birthday children always have crap garden toys because noone ever thinks to get garden things at that time of year, with the 'buy a big gift halfway through the year' plan that most December babies get, most do have slides and swings!)
The magic of Christmas and the magic of their birthday all get wrapped up together.
As they get older, and they want a party at their birthday rather than halfway through the year, you can be the parent the others love because you put on a party between Christmas and New Year, that's a week when fuck all is happening, children are beginning to get bored of the tree and seeing relatives, cabin fever has set in, and often it's raining - all other christmas parties happen before Christmas, a party to go to will get a good turn out (if unlike this year, half your guests aren't stuck with flooding as we found, but that could be a problem for any winter party!!).
Alternatively, if you put on a party they can 'drop and run' the weekend before Christmas, you will be a hero to the mums who are running round like blue arsed flies trying to get Christmas organised!!