What if my counsellor trying to convince me of something, that I don't believe is true

A counsellor should never try to convince a client of anything. He or she may raise an issue or suggest an interpretation (possibly on several occasions), but if you are sure that it does not apply, he or she should accept that it is probably best left alone. Take the example of someone who drinks alcohol because he or she believes it helps him or her to relax, and does not want to discuss this. This may be one situation in which the refusal to discuss an issue could bring into question the usefulness of continuing with a talking treatment, but even then this can be put to the client in a friendly rather than confrontational way. Bear in mind that discussing something is not the same as agreeing with it. You are entitled to stand your ground, and to tell your counsellor that you do not find something a useful subject to talk about.
Although this is rare, it may sometimes be necessary to point out to a counsellor that his models of working, and/or the questions he asks, do not match your expectations of what would be helpful. The sessions are for your benefit, not for an over-enthusiastic counsellor to talk about the kinds of problems or issue that he or she finds most interesting.