Q: Agree or disagree: The number of young people who live with their parents after they finish their education will increase in the future. (120 -150 words)

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I disagree with the idea that the number of young people who live with their parents after they have finished their education will increase within the years. ["More common" didn't fit to the overall context and made this paragraph lack a satisfying logical construction. You can add "within the years" to make the sentence seem and sound less vague.]

First, considering people's will to be free [again, "First, considering personal freedom" seemed and sounded a bit vague. You shouldn't be considering personal freedom as a whole in this part. Considering people's desire to be free seems more suitable.]. If one lives with their parents, their behavior must be under their parents's consent. For instance, one could have a girlfriend and want to live with her, which they couldn't do if they were living with their parents, because it could bother them.

Second and most important, living with your parents may shut the door for future job opportunities. For example, one can live too far away from the company to work at it. [I didn't quite get your point here. Sorry.]

Therefore, I disagree with the idea. [Not wrong, but you have already stated that in the first paragraph.]