The defamation case, which was launched by Mr Greenwich over Mr Latham's statements, will proceed to trial next year after settlement talks broke down, the Federal Court heard on Tuesday.
The independent MP is suing over the graphic tweet, which came in response to Mr Greenwich calling Mr Latham a "disgusting human being".
Mr Greenwich claims the tweet "unleashed a torrent of really despicable homophobic and other abuse".
Mr Greenwich made the comment on Twitter after LGBTQI protesters were attacked outside a Sydney church hall where Mr Latham made a speech ahead of the NSW election in March.
The lawsuit targets both Mr Latham's tweet and statements made during an interview with the Daily Telegraph, saying the comments exposed him to "hatred, contempt and ridicule".
Mr Latham has denied that he defamed the independent MP and is vigorously defending the lawsuit.
On Tuesday, Justice Anna Katzmann noted the contents of the now "notorious" social media post.
Mr Greenwich's barrister Matthew Collins KC said his client was seeking aggravated damages after the tweet "unleashed a torrent of really despicable homophobic and other abuse".
"Mr Latham, our ultimate case is, responded in a wholly disproportionate and irrelevant and disgraceful manner," he said.
Instead of doing the honourable thing by apologising for and withdrawing the tweet, Mr Latham then "doubled down" on his comments during the Daily Telegraph interview, Dr Collins said.
Mr Latham argues Mr Greenwich's reputation remained the same regardless of what was said.
In that interview, Mr Latham discussed Mr Greenwich giving speeches about sexuality to students in schools.
"Mr Latham linked that in a disgraceful manner to conduct which was in fact understood … to be in the nature of grooming," Dr Collins said.
Barrister Barry Dean said Mr Latham was defending the case by arguing his tweet was a reasonable response to Mr Greenwich's initial attack and his comments were his honest opinion at the time.
He also argues there had been no serious harm done to Mr Greenwich, whose reputation remained the same regardless of what was said.
"When you look at the reputation of Mr Greenwich, that has not been affected in a material way," Mr Dean said.
Mr Latham is also running various qualified privilege defences and a defence that his comments were made in the public interest.
The matter will go to a five-day hearing next year, when both Mr Latham and Mr Greenwich will give evidence.
Other witnesses will also be called to discuss the character and reputation of Mr Greenwich.
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