It's just that the 'Well, *I* would do such and such' can sometimes come off as guilt-tripping, or as saying your choices should be what the 'right' thing to do is. That's not always true, sometimes it does seem more like sharing experiences and perspectives. But, the constant repetition of the father's age being 86 by multiple posters, and the emotionally-tinged phrasing about how he might die soon and just wants to see his family, is I think what people are responding to as guilt-tripping.
Sometimes there'll be a post discussing, oh, say, going to a family wedding, and people will say things like "I guess my priorities are different, because I would make every effort to go" and it just comes off as moralizing.
I think with the history of the OP's relationship with her dad, I understand her hesitancy. There are also two issues being conflated--the casual/in question nature of the invitation itself, and whether the OP should facilitate her father going.