How can one deal with parents' insistence on proposing to a girl whom he does not see as a suitable partner, and avoid their anger while trying to convince them of his point of view?

Obeying one's parents is obligatory, unless it involves disobedience to Allah or causes undue hardship to the children. If a mother completely forbids her son from marrying, or forces him to marry someone he does not desire, then there is no obligation to obey her in this regard. Parents do not have the right to compel him to marry someone he does not want. The best solution to this problem is to involve righteous people for mediation, to supplicate, and to turn to Allah.