Is Aegyptopithecus a monkey?

No. It predates the divergence of Old World Monkeys within its order:

Parvorder Catarrhini

Superfamily Cercopithecoidea

Family Cercopithecidae: Old World monkeys

Superfamily †Propliopithecoidea

Family †Propliopithecidae (includes Aegyptopithecus)

Superfamily †Saadanioidea

Family †Saadaniidae

Superfamily Hominoidea

Family Hylobatidae: gibbons

Family Hominidae: great apes (including humans)

Parvorder Platyrrhini: New World monkeys

You really should be asking in the appropriate section, or at least have the skills to google this kind of stuff. The inability to independently search the internet is a serious functional deficit in this day and age. Barring both those concerns, the answer is because aegyptopithecus existed before the divergence of apes and monkeys.

It's not a monkey, it's a catarrhine.

Monkeys' nostrils face sideways with a wide septum, catarrhines' nostrils face downwards with a narrow septum, like ours.

Because it looks more like a cat.

Monkey, yes. My uncle, no. Not sure about you.