Why would he lie about this 😒

My husband has a new, female, coworker. He told me she was being hired but said the other guy is supposed to train her. His exact words were they he's not interested in that responsibility.

However, not only did he lie about when she started, but he also lied about the fact that he IS training her.

His phone is old and stupid and he ends up accidently calling many people, me included. I don't listen in for very long, just a few seconds to make sure he's not in trouble or is actually looking for me or something.

Half the times I can hear them in training (him pretty much just talking about the job and what to do and her stupid giggles because he's nice and friendly and funny) and then today I heard him ask her how her first day yesterday was, but he told me she started a couple of weeks ago already.

I am very insecure due to past, minor infidelities in his part and I image he told me so I don't get paranoid and that but lying makes it so much worse.