Someone correct me if I'm wrong, I'm certainly not a lawyer, but didn't he have the right to defend himself from an armed civilian even if he did commit a petty crime?
The short answer is yes, but the longer answer is a judgement call from the jury.
Suppose you catch someone in the act of committing a petty crime. You demand that he stop. He doesn't stop. He takes off running. You pursue. You find yourself looking at him, and he is coming toward you. You have a gun. Now what?
The question before the jury may end up with whether or not a reasonable person in that situation would have a fear for his life. I am talking about "you" in the above example, i.e. the person who draws the gun after catching someone committing a petty crime. Does he have the right to pull the gun in order to threaten the petty criminal?
A jury will have to weigh all the facts, and the relevant law. However, juries don't always follow the law to the letter. They sort of substitute their own judgement about the circumstances. For example, suppose that the person committing the petty crime had a strong resemblance to someone who was on a wanted poster in the post office. The jury would weigh that, and their ultimate decision might end up influenced by whether or not the person actually was the person on the wanted poster.
In this case, there will be a lot of questions. If the jury believes that Mr. Arbery was actually an habitual offender, and the McMichaels were aware that he was an habitual offender, they are likely to believe that Travis McMichael raising his shotgun would be a reasonable response to the situation, and the McMichaels might get off.
The interesting thing, legally, in this case is that the actual killing of Mr. Arbery is only marginally relevant in this case. At the time of the struggle, there is no doubt that a reasonable person in either of their situations would perceive that their lives were in danger, and lethal force was justified. What will determine whether the McMichaels go free will be whether actions prior to the killing were the responsibility of the McMichaels, or or Ahmaud Arbery.
And I'm saying "the McMichaels", but there may be a difference in how they treat Gregory and Travis McMichael.
In my opinion, grabbing guns and pointing them at people is almost always a bad idea, and it seems to me the McMichaels ought not to have done that. However, if they can convince a jury that it was a reasonable thing to do, they'll go free.