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Your girlfriend has trouble trusting men. How can you convince her that she can trust you? You can't convince her to trust you. What you can do is be trustworthy.
The most common complaint of singles is that they are lonely. God didn't design us to live in isolation. Intimacy is one our deepest needs. If you're single, invest your time with others. It's the language of friendship.
Are you attempting to improve your marriage by trying to change your spouse? Matthew chapter 7 tells us not to judge others. Examine yourself and see if YOU are the one who needs to change.