Felix Ngole, 40, from Barnsley, says he was expressing a traditional Christian view and complained that Sheffield University bosses unfairly stopped him completing a postgraduate degree.
He lost an earlier fight when Deputy High Court Judge Rowena Collins Rice ruled that the university bosses had acted within the law, after a High Court trial in London.
Mr Ngole has now asked Court of Appeal judges to consider the case.
Three appeal judges on Wednesday finished analysing his challenge after a two-day hearing in London. They are expected to publish a ruling in the near future.
Mr Ngole felt his challenge was a “case for freedom”, appeal judges heard.
University bosses deny bias and say they did not act unfairly. They say Mr Ngole’s appeal should be dismissed.
Mr Ngole says his rights to freedom of speech and thought, enshrined in the European Convention on Human Rights, have been breached.
Lawyers representing the university argue that he showed “no insight” and the decision to remove him from the course was fair and proportionate.
They said he had been studying for a professional qualification and university bosses had to consider his fitness to practise.
Mr Ngole posted the comments in 2015, judges have heard.
He was taking part in a debate on a Facebook page about Kim Davis, a state official in the US state of Kentucky, who refused to register same-sex marriages.
WHAT DO YOU THINK?- We have all sinned and deserve God's judgment. God, the Father, sent His only Son to satisfy that judgment for those who believe in Him. Jesus, the creator and eternal Son of God, who lived a sinless life, loves us so much that He died for our sins, taking the punishment that we deserve, was buried, and rose from the dead according to the Bible. If you truly believe and trust this in your heart, receiving Jesus alone as your Savior, declaring, "Jesus is Lord," you will be saved from judgment and spend eternity with God in heaven.
What is your response?
If you are not a Christian, and would like to become a Christian. Simply say - "LORD Jesus, thank you for forgiving me of my SINs, today I am deciding to follow you. Accept me into your family, in Jesus name I pray. Amen "
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