In fact, that area - where Jews lived as well as Muslims before 1948, in quarters known as Shimon HaTzadik and Nahalat Shimon - was the scene of many Arab attacks in 1948 on their neighboring Jews.
Arabs from Sheikh Jarrah started attacking their Jewish neighbors almost immediately after the UN Partition vote. This article is from January 12, 1948, where it mentions that attacks had been coming from that area for three weeks already:
For the rest of the month, the Palestine Post had almost daily articles about attacks originating from Sheikh Jarrah at neighboring Jews:
In February, the attacks continued, including attacks on convoys headed towards Hadassah Hospital:
In March, attacks on innocents escalated. This is from March 28th, and the death of a Jew was barely mentioned:
While the British promised to protect hospital convoys, they did not take their jobs too seriously as they were planning to evacuate in May. In mid-April came the climax of Arab attacks on Jews, one that should have been foreseen given all the previous attacks:
Nearly 80 medical workers and others were slaughtered - and the neighborhood that spilled so much blood was known quite well:
It is interesting that this history of that neighborhood is not mentioned as today's media wants to paint the Jews as the aggressors - by savagely purchasing houses with Zionist cash and violently using a respected legal system to evict people who haven't paid their rent for years.
This history of real violence and aggression from the Arabs of Sheikh Jarrah just doesn't fit that narrative.
UPDATE: To make things clear, Sheikh Jarrah was both a sub-district and a neighborhood ("quarter") of Jerusalem. The sub-district included the quarters of Sheikh Jarrah, Hayy el-Huseyni, Wadi el-Joz and Bab ez-Zahira, and the Jewish quarters of Shim'on Hatsadik and Nahalat Shim'on.
The part that attacked the Jews was the Sheikh Jarrah quarter. The part that is now called "Sheikh Jarrah" that is in the news is actually the Jewish quarter of Shimon HaTzaddik.