Thank you for contacting JustAnswer.
I am sorry to hear that you are having such a difficult situation with your partner. Extended family issues can be quite difficult and can be very dangerous to a relationship. It sounds as if your partner has not been able to give you a reasonable and rational reason why he tries to avoid your family get togethers and that you see no clear problem with how they treat him. I wonder if there are other things that your partner behaves this way about, or if it is strictly related to events with your family.
You might try asking him if there is anything that you could do to make these family get togethers easier or more enjoyable for him. You may use this forum to let him know how important these events are to you and to perhaps prioritize that some seem extremely important while others might be more optional for him to decide if he wants to attend. Sometimes, writing about this type of issue to each other can allow the other person to be less defensive and more likely to open up. You may also want to ask him if there are any things that you do or don't do that cause him this type of frustrations to see if this may be a resentment being acted out on his part.
It seems as if the two of you have developed a pattern in which there is quite a bit of debate and discussion about seeing your family. I wonder what would happen if you began to simply invite him to attend with you and then went, with or without him, without arguing or over-discussing this issue with him. He may then decide not to attend any family functions (and then you would need to decide if this would be acceptable to you or not) or he may decide that he might choose to go to some or all of them. In any event, taking the emotional charge out of the situation by stopping the nagging, fighting and bartering, may change the impact of this on the relationship.
In the meantime, be sure to take care of yourself through healthy eating, exercise, rest and reaching out to supportive people in your life. I hope this is helpful. Please let me know if I can clarify further.