The only two reasons that I could see to do it would be to benefit from the gifted part of the house equity, but I am not sure that this would be allowable in the circumstances; and a desire to keep this particular house, which no one can comment on but the OP.
Can I ask who suggested this to you?
If I have understood you, this won't save your inheritance and the mortgage will cost you interest which may not be the most cost effective way of funding your father's care