Start with why does he have a 'man cave' Hate that term by the way. What does he hope to achieve in it?
From www.colour-affects.co.uk/psychological-properties-of-colours
'RED. Physical
Positive: Physical courage, strength, warmth, energy, basic survival, 'fight or flight', stimulation, masculinity, excitement.
Negative: Defiance, aggression, visual impact, strain.
Being the longest wavelength, red is a powerful colour. Although not technically the most visible, it has the property of appearing to be nearer than it is and therefore it grabs our attention first. Hence its effectiveness in traffic lights the world over. Its effect is physical; it stimulates us and raises the pulse rate, giving the impression that time is passing faster than it is. It relates to the masculine principle and can activate the "fight or flight" instinct. Red is strong, and very basic. Pure red is the simplest colour, with no subtlety. It is stimulating and lively, very friendly. At the same time, it can be perceived as demanding and aggressive.'
It's going to make the space look smaller than it really is and promote aggressive feelings.
If he absolutely won't be swayed, can you swerve towards a more red-brown terracotta type shade? Or better a warm creamy beige background and then all the accessories in a browny brick red.