Sorry, if a guy doesen't trust me, he shouldn't ask me to go out with me. I am not going to "prove" that I can be trusted. That is bullshit.
The reason that I have this opinion is this: I have been out with a number of guys in my time, who shortly after we started going out, started doing things like, going through my phone and reading my text messages and seeing who had called and who I had called, turning up at places where I had said that I was going to visit friends to "check that I was there," listening to my phone calls from around the corner of the lounge room, or some similar place, ringing friends to see if I was there or had been there, and insisting that I call them and let him know if I wasn't going straight to or from a place. The reason given in all cases was that an ex-girlfriend had been unfaithful and that they didn't trust easily and that I had to "earn" their trust. I told them all to go fuck themselves. If they had trust issues over something in the past which had nothing to do with me, then they had no right to be in another relationship or even looking for someone to be in one with. They have no right to force their own issues on someone else. It is a case of putting your bullshit on someone else. To tolerate that shit is to enable it, and I won't do it.
In saying that, I don't trust perfect strangers or people I have just met not to rip me off, but that is a whole other thing entirely.