Is it acceptable or your SO not to be open and honest with you even though you are with them?

I tell my partner anything and everything. I believe it is healthy that he knows me and my life. However, he omits things like small details of his life. For instance, he said he went to pick up his check because they weren’t ready during his shift earlier that day. What he didn’t tell me is that he had asked a female coworker to pick it up for him and they met up so he could get it. He also has a “secret” he doesn’t want to tell me because he thinks it might change the way I see him. I have told him something extremely personal not because I wanted to tell him but because he continuously pressured me until I did. I wasn’t ready to talk about it but I told him because I felt that in order for this to work we should be completely honest and open as I have been. Please let me know what you think. I would greatly appreciate any input you have on this topic.