Headcanon that McGonagall is offended on a personal level that Umbridge loves cats.
Ok, but imagine McGonagall in cat form, prowling around the castl, in strategically chosen places so that Umbridge will come across her.
Umbridge takes the cat back to her office and feeds it a little saucer of milk.
The cat starts coming back to Umbridge's office around the same time every night, until eventually Umbridge gets into a little routine of setting out a saucer of milk for the cat before bed.
McGonagall now has all the best secrets on Umbridge, all of the results of evaluations, and most importantly, is in perfect position to spy on the ministry for the Order of the Phoenix.
All because Umbridge is obsessed with cats.
Like,
McGonagall: I will take the for of a fluffy little kitten.
I will let you think that I am a fluffy little kitten.
I will wait while you come to love and care for that kitten.
And then one night when you are sleeping.
I will steal into your home.
And punch you in the face.
