In The Mill on the Floss, why did Philip not get up to shake hands with Tom?

When Tom Tulliver returns to boarding school on a cold, wet day in January, he is introduced by the schoolmaster, Mr. Stelling, to a new classmate, Philip Wakem, who, like Tom, is from the town of St. Ogg. Despite being from the same town, the two boys do not shake hands. George Eliot sets up the scene as follows:

Tom felt in an uncomfortable flutter as he took off his woollen comforter and other wrappings. He had seen Philip Wakem at St Ogg’s, but had always turned his eyes away from him as quickly as possible. He would have disliked having a deformed boy for his companion, even if Philip had not been the son of a bad man. And Tom did not see how a bad man’s son could be very good. His own father was a good man, and he would readily have fought any one who said the contrary. He was in a state of mingled embarrassment and defiance as he followed Mr Stelling to the study.

For his part, Tom feels uncomfortable around Philip because the latter has a physical disability and also because he disapproves of Philip's father, the formidable Mr. Wakem. Tom is being unfair to Philip and judging him on the basis of his "deformed" appearance and his dim view of Philip's parent. He is unable to see Philip as an individual apart from his being hunchbacked and having a father who is different than his own father.
Philip politely rises when Tom enters the room and gazes at him with trepidation and shyness. He is unable to shake hands with Tom because of his fear and his pride:

Philip was at once too proud and too timid to walk toward Tom. He thought, or rather felt, that Tom had an aversion to looking at him; every one, almost, disliked looking at him; and his deformity was more conspicuous when he walked. So they remained without shaking hands or even speaking, while Tom went to the fire and warmed himself, every now and then casting furtive glances at Philip, who seemed to be drawing absently first one object and then another on a piece of paper he had before him.

This scene is a portrait of social disconnection and misunderstanding in the face of prejudices (on the part of Tom) and a commingled sense of pride and fear (on the part of Philip). Eliot is concerned with representing the conditions under which trust and mistrust are generated.