it could be a number of scenarios.
Firstly, were their ages recorded as 'of full age'? This means they were over 21 and did not need parental consent to marry but it could also mean they lied and had eloped. Were they married in the brides' Parish? It could be that she was actually illegitimate and the groom did not put his father's name on the banns to make her feel equal ,
Did they marry by registrars license in a non conformist church or catholic Church? maybe again the parents did not approve.
Did they marry in a register office? is their condition given as batchelor and spinster or widow/widower?
Who were the whitnesses? anyone with the same name as either of the couple? usually it would be, if it wasn't it may mean they were estranged from their families.
The clues are in there somewhere.
Where were they both on the 1851 census before they married? Were they with family or in service?
Where did they live on the 1861 census? Did any of their family live near them then?
the groom may have been brought up as the son of his Mum's husband, but he may not have been the natural son, have you found his baptism? if he was born after July 1837 he may even be registered with the GRO. If he was not baptised as the natural son of the man who brought him up he would not have perhaps felt good about listing him as his father in a church marriage register.
If you study each part of the certificate and relate it to other sources you may find a reason this happened.