Linguistically it's called a "copula", and, in Latin too, the verb "to be" links 2 things that are equivalent
(and thus, they never takes the accusative.)
I don't know Tagalog yet, but I know Indonesian, and it's the same language family, it's close.
I think "to be" is "pagiging" in Tagalog.
In Indonesian, it's "adalah, it'sa verb, but an optional verb, you can leave it out from the sentence, but it's still a verb. I think in Tagalog it's the same, I don't know why you think it's not a verb.
When the verb is omitted in Indonesian, I believe it's still considered as a copula.
Italian bloke here. This course has questionable pronunciations for some words. This one, for example, is supposed to be ma-ji-stra. Although we can't prove it with complete certainty, letters in Latin were read by our ancestors much like modern Italians read them today, so at least it should be based on our pronunciation models, not the Anglo-Saxon ones...