Ideas
When trying to complete the last level of the friend of animals aspiration, I will complete a task (ex play with two ghost cats or dogs) but my aspiration panel will still say 0/2. I've tried the other tasks as well (ex "be friends with 12 animals at the same time [3/12]"; or "feel the love from 8 different animals [3/8]" [I have 3 pets in this household]). Any animal friendship outside the household does not register in these aspirations. I play PC, unmodded, no CC. The character that I'm having trouble with was created in CAS. When I use "testingcheats true" and then "aspirations.complete_current_milestone" to try to force the aspiration to complete, I get satisfaction points, but the life aspiration objectives remain (although, I admittedly may not understand if that's exactly what that cheat is supposed to do).
The cheat doesn't seem to actually mark the goals as done (which does make sense to me as you haven't done them), it just finishes the aspiration. There is a bug report here: Aspiration Goals Not Checking Off | EA Forums - 11983733 where they are considered done but are not.
Have you tried travelling too ? Sometimes it doesn't register properly until you done that.