The title says it all, a friend told me that after jogging is necessary to stretch arms and legs, But is this true?, I don't find that the muscles of the arms work enough to need stretching.
It is not true. It is not necessary to stretch your arms after a run.
Out of all the physical interventions we utilize today, stretching has the least amount of evidence behind it. This is secondary not only to our poor understanding of the mechanism through which a muscle may or may not be lengthened, but also our generally poor in vitro measurement tools.
For those who thought this point was merely opinion I'm attaching an article. It is the American College of Sports Medicine's Position Stand on current evidence published in 2011. You will notice a preponderance of "C" and "B" grades under Flexibility Exercise in Table 2 which is in direct contrast to "A" and "B" grades for the other categories of physical intervention. I hope this clears up my statement.
If someone is about to put a muscle group through a very strenuous exercise, stretching or warming up that muscle group beforehand can help prevent injuries.
If someone has already put a muscle group through a strenuous exercise, stretching that muscle group afterwards will help dissipate any lactic acid buildup from the exercises.
Running, from what I have experienced, does not put your arms through any sort of strenuous workout.
...unless you are doing something different from most people.
So: No, there is no need to stretch your arms after jogging.
That said, it doesn't hurt either.
It depends largely on your goals. Some people desire muscles that are elongated (for lack of a better word) as opposed to bulky. To accomplish this, stretching is a very central tool.
When jogging, certain parts of the exterior musculature are engaged, such as biceps to bend your arm at the elbow, and shoulders to move your elbows back and forth. During the course of a run, these muscles will almost certainly have been warmed up to the extent that they can be purposefully stretched.
The only thing you'll need to consider, is whether or not stretching accomplishes a goal you have. As such, it's not necessary, to answer your title question. It's just something you can do, if you wish.