On the other hand, with all due respect to them, a chubby child may take all the lessons he desires yet it is unlikely he will ever become a great gymnast seeing he hasn't the natural build which favours it.
Made.
Olympic medalists like Svetlana Khorkina and Sandra Izbasa are tall for the average gymnast (shorter gymnasts ~1.55m are preferable since the impact of landing is smaller). However Sandra has managed to get two gold medals, one in 2008 and one in 2012. She worked extremely hard to overcome her height disadvantage. Same goes for Svetlana.
Top gymnasts aren't born flexible or strong either. Look at Nastia Liukin - she has so little strength but worked so hard to get her double front tumble (since it was compulsory). And flexibility can be trained. Nobody is born unflexible. Give it a year and I guarantee anyone can do a split.
At the beginner level, being naturally flexible or strong or good at balancing will give you a head start. At the elite level, it won't help. Everybody trains five hours a day, six days a week. Natural talents won't make any difference. Does this answer your question?
I would say they are made. As a coach( not gymnastics) I see how the extra nurture can help a player strive. You can be born with a certain amount of ability but it takes work and dedication to become great.
NO, you don't have to be born one. you can just practise and be able to the tricks (practise!) but some people are born with a thing called hypermoble (which i have) which makes your muscles more..."stretchy" but you can easily learn to do gymnastics, dont you worry!
People have instincts to survive and procreate. They do not instincts for the pommel horse or uneven parallel bars.
Certainly natural talent helps, but natural talent alone won't work past the club level.