Juhel Miah, 25, told BBC Wales: "All I want is a reason, I want to know why they kicked me off the flight."
Mr Miah had flown to Reykjavik, Iceland, with the party from Llangatwg Community School in Aberdulais, Neath, before boarding an onward flight to New York on 16 February.
But before the plane took off he was escorted off by security staff.
First Minister Carwyn Jones has written to the Foreign Secretary Boris Johnson for "urgent clarification" in the case, and Neath Port Talbot council has written to the US Embassy to "express its dismay" at the treatment of Mr Miah.
In the letter, Mr Jones says he understands Mr Miah was "escorted from the aircraft by US Homeland Security personnel".
The US Embassy in London has been asked to comment.
Mr Miah, whose first name is Mohammed but is known as Juhel, was in charge of eight pupils at the time and said there were a total of 39 pupils and five members of staff on the trip.
The teacher, from Swansea, who says he has a visa which is valid until 2019 and does not have a criminal record, said: "Everyone looked at me like I'd done something wrong.
"It made me feel really small, even though it shouldn't have. I repeatedly asked on what ground they were kicking me off the flight, no-one could give me an answer."
Mr Miah said he has a British passport and does not have dual nationality. His family's ethnic background is Bangladeshi.
"I can't think why they wouldn't want me on the plane, apart from maybe because I'm a Muslim," he said.
He added that he had never been to any of the seven Muslim-majority countries included in an executive order signed by US President Donald Trump, temporarily barring people from those places.
A federal judge in Seattle has since suspended the ban nationwide - a ruling which was later upheld at an appeals court hearing in San Francisco.
Mr Miah, who teaches maths at the 700-pupil school, said he was also denied access to the US Embassy in Reykjavik.
He said if he was not given a reason for what happened, he "would like someone to put their hand up and say 'sorry, we made a mistake'."
A council spokesman said: "No satisfactory reason has been provided for refusing entry to the United States - either at the airport in Iceland or subsequently at the embassy.
"Understandably he feels belittled and upset at what appears to be an unjustified act of discrimination."
The Muslim Council Wales said it was "deeply troubled" by what had happened, adding that such incidents "undermine equality and civil life".
The Foreign and Commonwealth Office said it was "providing support to a British man who was prevented from boarding a flight in Reykjavik".

Amond, 28, scored 33 goals last season for Grimsby as they won promotion through the National League play-offs.
"There were a lot of clubs in for him but we're delighted that we've managed to tempt him to The Vic," said boss Craig Hignett.
Former Chelsea trainee Woods, 26, joined in 2014 from Harrogate Town and has signed an undisclosed deal.
He has made 42 league starts for the club over two seasons, having missed the latter stages of 2014-15 with injuries to his ankle and fibula.
"Michael is a terrific player and I am delighted we have managed to get him sorted," added Hignett.
Find all the latest football transfers on our dedicated page.
A Muslim teacher denied entry to the United States while on a school trip said he has still not been told why.
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Hartlepool United have signed striker Padraig Amond and agreed a new deal with midfielder Michael Woods.