Wait it out or LEAVE?!

I(24)have been seeing this guy (32) about a month now and I have some concerns. 1. We went to adopt a pup for him and he decided to put a video (myself/pup together) on SC. His older niece saw this and he "jokingly" said that I was an ASPCA worker. His niece obviously didnt believe him, but that totally rubbed me the wrong way. This was brought to his attention, but he said that he is just very secretive with his family. 2 His BFF texted him last night to see if he wanted to meet up and he texted back "Damn, I cant I'm with this girl."(I saw this momentarily because he was holding his phone up towards the TV). Now, Its only been a month, and he has told me that he is very private about his life, but I am beginning to feel like I am non-existent. Now we do a lot of things together, a lot of things that couple do, so I dont understand why the secrecy? He knows that I have told my friends (close ones) and my mom. I dont see why its so hard to say this is my friend...And I dont know how to address this...what do you guys think?