How does setting the voting age at, say 28, rather than 18 or 21 make it not a Democracy?
Because you're denying adults who are supposed to be equal under the law their basic rights, obviously. It's undemocratic age discrimination if you deny the right to vote to people who have reached the age of majority.
Voter discrimination amongst adults based on their age is no more legitimate than voter discrimination based upon their skin color or sex.
Why is it OK to deprive 20 year olds the right to vote, if voting age is set at 21,
It isn't.
or denying 17 year olds to vote if voting age is 18,
Because 17-year-olds are minors who have not reached the age of majority. The essence of liberal democracy is the premise that all persons who have reached the age of majority are equal; that doesn't mean you give all rights of adults to minors, you means you give equal rights to all adults.
Apparently, by Sci's reasoning, the U.S. isn't a democracy because most of the rights and responsibilities of adulthood are conferred at age 18 -- but you can drive a car at 16 and you have to wait until you're 21 to legally consume alcohol.
A strange leap to make. Denying 18-, 19-, and 20-year-olds the right to drink does not mean the United States is not a democracy, because the relevant question -- "Are they adults whose basic right to vote is respected?" -- is "Yes."
However, 18-, 19-, and 20-year-old adults are discriminated against unjustly by denying them the right to consume alcohol, yes. There's no logic in saying you can fight and die for your country at 18 but not have a beer.
Setting different legal ages for different activities isn't age discrimination,
No, but denying adults basic rights is.