Why did the Muslims take Palestine?

Answer 1
Allah Almighty sent about 1,24,000 Prophets (May peace be upon them all. Hazrat Muhammad (SAW) was the last Prophet. The Muslims believe in all the holy Prophets. Most of them were born, and are buried in Palestine. Thus it is a very sacred land for the Muslims. The Muslims took over this alnd for this reason. Although, it is also considered sacred by the Jews and the Christians.

Answer 2
There was no specific "taking of Palestine". Between 634-638 C.E. Caliph Omar led a war of conquest against the Byzantine Empire to take all of the Levant (Israel/Palestine, Jordan, Lebanon, and Syria). Caliph Omar did not have to justify this expansion and conquest. The Muslims (including Caliph Omar) perceived that conquering neighboring territories was their duty as pious Muslims.

Historically, there was the "Right to Conquest" which was a pervasive idea in political thought. The idea was that it was natural for any country or state to grow and control more territory as it grew stronger. This allowed weaker states to dissolve in place of ones that were better run, a bureaucratic version of "survival of the fittest". The "Right to Conquest" prevailed as the dominant theory of nation-building until the mid-1800s when people started bringing up the concept of self-sovereignty and ethnic nationalism, which held the idea that people should govern themselves even if they are not the most powerful in the world. This view of state sovereignty has become dominant today and the Right to Conquest is seen as incorrect.

Since the Caliphates existed well within the Right to Conquest Period, the Caliphs did not have to assert a reason to conquer neighboring territories in Southwest Asia. It was their natural prerogative.