While both Arabic and Hebrew are Semitic languages, they are relatively distant from one another and not mutually understandable. I am a Hebrew speaker and reader/writer, but cannot understand the spoken Arabic dialect spoken by some of the local Arab speakers, except for a few words. Note that there are many spoken Arabic dialects as well as Literary Arabic which is common but not normally used in speech. Many Arabic speakers in Israel also know Hebrew, but native Hebrew speakers (Jews/etc.) usually do not have the motivation to learn Arabic or retain their knowledge of it.

Some other notes:

1. I studied Literary Arabic for 6 years in junior high and high school and passed the 5 points matriculation exam in it. However, I lost most of my vocabulary due to lack of use, and also do not readily remember some of the grammar.

2. A few Arab Israelis I spoke with told me it was easier for them to learn to read and write Hebrew than it was to learn Literary Arabic, despite the fact that the local Palestinian Arabic was their mother language. This is due to the diglossia present there.

3. If you know both English and Arabic, I can highly recommend listening to Shaike Ophir’s "The English Teacher" skit.