Same-sex marriage should be legalized because it is uncivilized to deny homosexuals their civil rights. The Constitution guarantees everyone equal rights and opportunities, however, s are denied both in terms of marriage.

is this better? I have support in other paragraphs

2 answers

Yes, this is much better. :-)
Be sure to put a semicolon (;) after "opportunities" not a comma. Otherwise, it's a run-on.