Why didn't obama serve? What was his excuse for not enlisting?
I have no special insight into Obama's mind, and it's unclear why you're asking me to explain his thinking, or why Obama's actions in this instance really matter or why they are an "excuse" for Donald Trump (then again, Trump does have a habit for blaming others for everything).
Anyways, let's just assume that the answer to your question is that
Obama simply didn't want to serve in the armed forces. So what? Obama doesn't need an excuse: there was no legal requirement or obligation to enlist or serve that Obama skirted; we have a volunteer system, after all. Again let's assume he didn't want to. You can certainly choose to hold that against him, if you so want, but he doesn't need an excuse.
The situation with Donald Trump, as presented, however, is
different: at the time of this incident there was a draft, and people were called up, by the draft board, and, effectively, ordered into serving, whether they wanted to do or not. They had a
legal obligation to report when drafted and when Trump's number came up and he was called to serve he didn't.
If his medical deferment for bone spurs was received through his Father's influence and wasn't a legitimate medical problem, he basically cheated the system and violated the law. Did he? I don't know, but it wouldn't surprise me. Plenty of others did (some using the same medical deferment trick, and some went so far as to flee to Canada

). And, really, who can blame them (and Trump) for trying to avoid it? Who
really wanted to walk into Vietnam, to be cannon fodder in a meaningless war?