It's always better when it's their idea.
My dad was a great pianist. He often played in the house and I'm sure I would have eventually been interested enough to ask for lessons. It wasn't my idea, however, when I was 6, and all we have to show for it, to my everlasting regret, is two years' worth of wasted money.
But I do have to credit my parents for instilling an interest in music and for being fully supportive when I chose to start drums at 15. When it was "drum time," there was never a "shut up" from them or my siblings, and it couldn't have been pleasant, even when I finally figured out what to do.
Another hard lesson learned, but for kids who are just starting out on drums, I suggest establishing a timetable for success with a snare drum before going all in on a drum set. Success means not only progress (which will differ for all students), but a commitment to practice, which includes being able to maintain schoolwork and other family responsibilities.
Find a teacher who can not only teach the rudiments, but can provide real-world examples of why they are important (I wish we had YouTube back in the day).
Don't get me wrong: I'm glad I play and I can hold my own, but I sometimes wonder how much better I'd be (and what playing opportunities might have come my way) if I'd been more serious about drum (and piano) lessons.
Al
