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.
Mr Ngole said he had argued that Mrs Davis's position was based on the "Biblical view of same-sex marriage as a sin".
He said he was making a "genuine contribution" to an important public debate and he was "entitled to express his religious views".
University bosses said he posted comments on a publicly accessible Facebook page which were "derogatory of gay men and bisexuals".
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