Four of Mr Carmichael's constituents raised the case under the Representation of the People Act.
They said the MP misled the electorate over a memo which claimed SNP leader Nicola Sturgeon wanted David Cameron to be re-elected prime minister.
Roddy Dunlop QC asked judges at the Court of Session to dismiss the case.
He told the specially-convened election court that the petition was "irrelevant" and "bound to fail".
However, Jonathan Mitchell QC, representing the petitioners, later told the court that his clients believed that Mr Carmichael leaked the information to deliberately smear the SNP.
The court heard that this was to reduce the chances of a Scottish National Party candidate being elected in Orkney and Shetland.
The case, believed to be the first of its kind in Scotland for 50 years, arose from remarks made by Mr Carmichael at the start of the general election campaign in April.
The MP, who had been Scottish Secretary in the Tory-Lib Dem coalition before the election, authorised leaking a civil service memo suggesting the first minister had told the French ambassador she backed Tory PM David Cameron to remain in Downing Street.
Mr Carmichael had initially denied leaking the confidential memo to the Daily Telegraph.
He claimed the first he had heard of it was when he received a phone call from a journalist.
However, the MP later admitted full responsibility for sanctioning its release, and accepted the "details of the account are not correct".
Mr Carmichael was not in court for the hearing.
His QC, Mr Dunlop, said Section 106 of the act forbids election candidates from making false and statements about their rival candidates.
He stressed that a false statement of fact must be "directly related" to the personal character or conduct of a candidate.
Ms Sturgeon, the leader of the SNP and Scotland's first minister, was not a candidate in May's general election.
The QC said it would have been the "easiest thing in the world" for the Act to make it clear if a false statement could be about non-candidates.
He also said attacking the political position of a candidate did not necessarily attack their character.
Mr Dunlop said the case put by the petitioners "flies in the face of the authorities" and was "wrong in law".
The QC said that if the petitioners were right then court would get a lot busier, as all that would be needed was a dispute during an election with one false answer.
He said if this was the case then any prospective MP in the run-un to an election would have to be strapped to a lie detector and administered with a truth serum.
Mr Mitchell representing the petitioners seeking to remove Mr Carmichael from office, said the MP did not dispute that he made certain statements of fact which were false, or that the statements were made before or during an election.
However, Mr Mitchell said Mr Carmichael did dispute that he was attempting to affect the return of a candidate, as the petitioners claim he was.
The hearing before Lady Paton and Lord Matthews continues on Tuesday.
This is the first parliamentary election petition to be brought in Scotland since the Grieve V Douglas-Home case of 1965.
That saw Scottish poet Hugh MacDiarmid - who was born Christopher Murray Grieve - attempting to unseat former prime minister Alec Douglas-Home who at the time was MP for Kinross and West Perthshire.
MacDiarmid had claimed that the Conservative politician's election was void because he had participated in a national party election broadcast on behalf of the Conservative Party and had declared the costs of this on his election expenses.
The court found that no offence had been committed, either by the candidate or the broadcaster.

Kerosene leaked from a pipeline near Nantycaws, Carmarthenshire, into nearby Nant Pibwr, with dead fish spotted.
The Welsh Government said the A48 will close in both directions from the Nantycaws turning to Carmarthen from 19:00 BST on Friday until 06:00 Monday.
Traffic will be diverted through Nantycaws and Llangunnor.
Rural Affairs Secretary Lesley Griffiths visited the site of the spill on Saturday.
In a letter to assembly members, she confirmed the scale of the spill was bigger than previously thought.
A legal challenge over the election of Liberal Democrat Alistair Carmichael as Orkney and Shetland MP should be dismissed, his QC has claimed.
[NEXT_CONCEPT]
Details of when a main road will close for repair work to a damaged fuel pipeline that leaked more than 140,000 litres of oil have been confirmed.