Is it permissible to marry a man whom the mother rejects for an unconvincing reason, with the mother insisting on her disapproval and the son insisting on the marriage, and is it necessary to withdraw from the marriage to appease the mother?

The suitor is not obligated to obey his mother in abandoning the marriage to you if she refuses without a valid reason, and he would not be disobedient by disagreeing with her. Similarly, it is not forbidden for you to marry him despite his mother's refusal, even if her obedience in this matter were hypothetically obligatory, as the marriage would be valid. However, the suitor is advised to strive to convince and appease his mother, and it is not advisable to disobey her command. If you wish to break off the engagement for fear of the consequences of the mother's refusal, there is no blame upon you, and you should consult wise family members and perform Istikhara (prayer for guidance) before proceeding with the matter.