I am in a dispute that is heading toward lawyers and I want to win it. Is it wrong for a Christian to take someone to court, or am I allowed to fight this?

“Go not forth hastily to strive, lest thou know not what to do in the end thereof, when thy neighbour hath put thee to shame. Debate thy cause with thy neighbour himself; and discover not a secret to another:”

The advice here is procedural: do not rush out to argue your case in public, because you may find yourself shamed when the other side answers. Take it up with your neighbour directly first. Israel's courts sat in the town gate in front of everybody, so going public was a genuine escalation with an audience attached. Proverbs is not against justice. It is against making the most expensive move first.

“Now therefore there is utterly a fault among you, because ye go to law one with another. Why do ye not rather take wrong? why do ye not rather suffer yourselves to be defrauded?”

Believers in Corinth were suing each other in front of pagan magistrates, and Paul is exasperated, largely at how it looked from outside the church. He asks a question rather than issuing a ban: why not rather accept the wrong. That is a question about what you are willing to lose, not a rule that Christians may never use the law. Crime, abuse and serious injustice are not what he has in view.