Little “white lies”

I’ve been with my bf for two months.. and I’m constantly catching him in little white lies, and I can tell he lies when he stutters.. about how “busy” he is. Or he has school and when I call him at the time (I forgot) he returns my call which I ask I’m sorry I thought you had school and he replies “oh... it got pushed back”.. just a lot of white lies I don’t know if I should be worried?

Example-

Today in the morning he had errands and when we got on the phone he said he went to the bank, two hours later we just got off the phone and I had asked oh babe what have you been up to.

“Oh I went to the bank” and o was just like? I thought you already went?

He stutters and says oh I forgot to do something else.. but it’s constant

Plenty of more examples.

He would tell me one thing about his past, just talked to his sisters and they said something completely different and he just stood quiet