Can Airline Legally Refuse Boarding for NO Reason?

United contract of carriage has a list for

UA shall have the right to refuse to transport or shall have the right to remove from the aircraft at any point, any Passenger for the following reasons

including

Passengers who fail to comply with or interfere with the duties of the members of the flight crew,

Let me break this down to make it easier understand

Passengers who fail to comply with the members of the flight crew,

that is pretty close to "Simon says". And since US federal regulations have similar wordings, all other US airlines will be happy to kick you off if you don't do what the crew says (you might even get into prison for it).

With regard to the EU, yes.

The EU regulation (261/2004) acknowledges that a passenger can be denied boarding against their will and sets out the rights of the passenger to compensation and accommodation, but does not restrict the airline in reasons for denying boarding against the passengers will.

The regulation also sets out situations in which the airlines liabilities are limited.

http://eur-lex.europa.eu/resource.html?uri=cellar:439cd3a7-fd3c-4da7-8bf4-b0f60600c1d6.0004.02/DOC_1&format=PDF

Can Airline Legally Refuse Boarding for NO Reason?

Technically, yes because the aircraft is private property. However, they would still be bound by the Contract of Carriage. But, the conditions are so broad that they will argue that any reason is covered by the CoC.

Operationally, no, because any denied boarding has to be logged and a 'reason' noted. But, that 'reason' can be as nebulous as concern by the flight crew.