You needed to be a male citizen landowner. But part in this is because eligibility to vote was eligibility to be assigned political office. Voting wasn't just a right, it potentially came with duties as well.

It's not that illogical to exclude slaves because a slave in office gives their masters influence over an official, exclude people without land because they were susceptible to bribery, and exclude women who could get pregnant.

Aristocracy with no election at all is not _that_ illogical either. But, it takes some seriously twists to call it democracy.

> exclude people without land because they were susceptible to bribery

This however means, Athens dont put other democracies in shame at all.

Why is universal suffrage necessary for democracy?

Because otherwise you decide that segments of the population shouldn't be heard. Democracy is literally "government by the people" - anything but universal suffrage means you consider some part of the population not people.