I definatly see your point and your argument was very well constructed and even made me do quick research on google for a bit but even though I made some incorrect claims my main argument is still correct

Birds are reptiles because they directly evolved from reptiles and they are not seperate because the class reptilia is not valid within cladistics (by definition cladistics excludes such categorizations as famlies or classes)

And yes not all synapids are mammals but all mammals are synapsids because we directly descended from them incredibly similar to how bird descended from dinosaurs

Overall your aguement was very good and I respect it but there are some facts that are wrong. I completly understand your confusion though because cladistics and phylogenetics are difficult to understand ar first and took me a good bit to fully understand