My loner seems to be perfectly happy with her dog.
She also has the dog lover trait though, if I remember rightly. The dog has the intelligent trait, so they do training and have intellectual discussions.
As a loner I can confirm that even a spider on the ceiling can cause stress by too much socialisation under the right circumstances (having had too much social interaction right before seeing it). Admittedly that's rare and I laugh about it now, but it did happen. Pets can easily remove a happy to be alone moodlet irl.
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A similar problem occurs with paranoid Sims, they are getting tense from two pets interacting with each other nearby the paranoid Sim.
This is funny, lol. Imagine being stressed out by feeling that nearby pets are plotting something evil against you.
She also has the dog lover trait though, if I remember rightly. The dog has the intelligent trait, so they do training and have intellectual discussions.