Is it OK for my boyfriend to google everything about me? and dig deep into my past?

I am a bit more experienced in the dating department, than my boyfriend. he's been with someone for the past 4 years. but I recently found out he googled my name, my nickname, and screen names I use for sites. and apparently there's still things about with me and exes. like photos, or MySpace things, or blogs. and when I tell him "that was before you it doesn't matter" he says "if it doesn't matter then you should tell me." like I'm hiding things from him. I love him with my whole heart but he just digs and digs what should I do?
Is it OK for my boyfriend to google everything about me? and dig deep into my past?
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