McGill is one university. There's also Concordia, UQAM, UdeM, Polytechnique, etc. There's about 350,000 students living in Montreal;
the greatest number of students per capita in North America.
People may want to live in Vancouver, but the issue is less that too many people want to move there, as there is still much constructed, and moreso that so much new construction goes to foreigners who don't actually live in Vancouver. This drives up the cost of real estate for those living there, leaving people artificially priced out of the market.
Climate is subjective. Vancouver has a mild summer, Montreal has a hot summer. Vancouver has a wet winter, Montreal has a snowy winter. Snow has not prevented cities like Minneapolis from succeeding. For people who actually enjoy heat, Montreal is probably a better fit.
Since you brushed over it, I'll repeat that Montreal's cultural offerings dwarf anything Vancouver offers. It's simply no competition. Now, granted, it's kind of an unfair comparison, seeing as Montreal is far older, more established, and has the English-French duality to it.
In terms of location, again subjective. Montreal is closer to European and emerging African markets, and is embedded in the metropolitan Eastern North American region, which includes New York, Boston, Washington, and Toronto, all of which are more important connections than Seattle or Portland. Beyond cities, Montreal is home to true winter activities, even outside of the mountains, and has great outdoor opportunities, even if Vancouver does excel here overall. Vancouver is also closer to Asian markets and California, which, depending on interests, may be a bigger deal for you.