The Abrahamic god actually evolved over time. At the beginning, God was just a tribal god. There were various tribal gods, with God being just one of them.
The followers of God, those who would be later called the Hebrews, split off from the other tribes (the evidence shows that most likely they were part of the Caananites, and split off of them) and wanted to differentiate from them.
Now, it is known that the early Hebrews were not monotheistic. They did have their own personal god; however, they also believed that there were other gods. Some Hebrews even worshipped other gods. The problem though was that God's prophets and priests claimed that their god was more powerful. Part of this could have been a monetary one (so more people would sacrifice to their god) or simply an ego thing, or even possibly because they truly believed it. For whatever reason though, God's prophets really battled the other gods.
It was in this struggle that the idea that God was jealous, or that he was called jealous was formed. Mainly, it was his prophets trying to gain a monopoly over god that caused them to state that God was a jealous god. It was a logical move, basically telling everyone else that they were wrong, and that God was going to wreck havoc with them if they did not obey.
That God though is not the same as the current God though. At that time, the idea of God, or God was still forming to what he is now. It took a long time for God to be what he is. Much of it had to do with the time periods.