Why is {a} not transitive unless $a = emptyset$

I am trying to understand what transitive sets look like or what not transitive sets look like. I found another thread where someone stated that ${a}$ is not transitive unless $a=emptyset$. I don’t quite understand why this is the case. Off course $a in {a}$. But why is $a nsubseteq {a}$
(Source).
I have seen a video on YouTube where the guy stated that $F={F,G}$ with $G={F}$ would be transitive.
Those seems contradicting each other to me… (Source)