Saying “Ancient Greek isn’t dead because Modern Greek” is like saying “Latin isn’t dead because Spanish.” It’s related(-ish) to Modern Greek, but the differences are way beyond the point where most people would feel comfortable calling the two dialects of the same language. Beyond basic vocab stuff (νερό vs ὕδωρ, e.g.), there are also significant grammatical differences—Modern Greek has an analytical subjunctive and future (να/θα + verb), where Ancient Greek had synthetic forms (i.e. the verb itself changed). Ancient Greek was also rife with what are called particles, little words that are best (in my humble classicist-turned-linguist’s opinion) ‘translated’ as tone of voice, but often get translated as “as far as I’m concerned,” “on the one hand…on the other”, “while…”, and the like. Pretty big differences. I will say, one of my favorite things about Ancient Greek is that there were a bunch of different dialects, which seem more like what we’d call accents now (the differences seem mostly to be the equivalent of “soda”/”pop”/”coke”, “pahk the cah” kind of stuff), and everyone was hilariously catty about everyone else’s accent. To be fair, though, the Ancient Greeks were hilariously catty about basically everything.