What is the idiom/proverb for "the more you pressure someone they will run away from committing"?

In addition to the other answers, I want to add the Streisand Effect, even though it is not a complete answer to your question.

The concept is named for an attempt by singer and actress Barbara Streisand to have an aerial photograph of her property removed from a database being used for erosion research. Prior to this, only the researchers even cared about the database, but after her request was publicized, suddenly everyone wanted to know about it. The photo she wanted removed was instead copied to other places and viewed by many.

The idea is that if information is out there where anyone can get it, people generally tend to ignore it. But as soon as people are made aware that someone wants to hide or suppress the information, they have an instant desire to have that information. The linked Wikipedia article lists several other examples, and also links to the underlying psychological phenomenon.

Forbidden fruit is the sweetest.

It refers to the story in the Bible in which God tells Adam and Eve not to eat the forbidden fruit, but they are tempted and do so anyway. So, the proverb means that people are drawn to things that they are forbidden from doing or having.

Note that this proverb is for the second part of your idiom/proverb request. It's not about the situation when somebody is under pressure and trying to wriggle out of an engagement.