Both TP but no split?

Why are certain pots not split when both have a TP

For example, what I just experienced, and what made me decide to ask a question about that.
I had an A and so did my opponent, there was an A on the table, so both a TP.
the difference was that he took the pot.

Is it a matter of the better kicker?
Why is one pot split where both have a TP and the other pot not?

I looked in the game rules that could find online, but I can't figure it out
Can someone explain it to me?