With a dying rodent, it's kinder to kill it, so why do humans not deserve the same?

I know it's an age old question, but i do want to hear opinions, humans are forced to remain alive suffering and in pain on life support machines and spending their last undignified months in bed. Surely if your 80 year old grandad has an inoperable brain tumor, and every day is a struggle, it is so much more humane to allow him to be at home in his bed, without having been a burden for months, with his family surrounding him, and letting a doctor quietly and quickly giving him an injection to end it all. Why is it we are allowed to choose how we give birth and how a new life is to come into the world, but we aren't allowed to choose how we leave it short of jumping off cliffs? And why do we not get the same dignity animals get?