First of all, your stylist is wrong. Hair is growing ALL the time. A weave won't make it grow and neither will any other style. Weaves do help most people retain their hair because the hair is hidden away so it can't get broken off by daily styling and manipulation. But if you don't want a weave, don't get one. Sounds like the stylist just wants the extra money.
Second of all, it is possibly to have great retention without constant protective styling if your hair is really healthy. But most people find that they do need to do some type of protective styling, especially once they get to shoulder length. There are many different styles you can try so don't feel like your only recourse is a weave or a bun. Get creative.