Hadith: The Messenger of Allah (may Allah's peace and blessings be upon him) used to go by way of Ash-Shajarah and return by way of Al-Mu‘arras. He would also enter Makkah through the Higher Pass and leave through the Lower Pass.

عن عبد الله بن عمر رضي الله عنهما "أَنَّ رسُول الله -صلَّى الله عليه وسلَّم- كَانَ يَخرُجُ مِنْ طَرِيقِ الشَّجَرَةِ، وَيَدْخُلُ مِنْ طَرِيقِ الْمُعَرَّس، وَإِذَا دَخَلَ مَكَّةَ دَخَلَ مِنَ الثَنِيَّةِ العُلْيَا، وَيَخْرُجُ مِنَ الثَنِيَّةِ السُّفْلَى".
[صحيح] - [متفق عليه]

‘‘Abdullāh ibn ‘Umar (may Allah be pleased with him) reported: The Messenger of Allah (may Allah's peace and blessings be upon him) used to go by way of Ash-Shajarah and return by way of Al-Mu‘arras. He would also enter Makkah through the Higher Pass and leave through the Lower Pass.
Sahih/Authentic. - [Al-Bukhari and Muslim]

Explanation

The Hadīth of ‘Abdullāh ibn ‘Umar )may Allah be pleased with him) highlights the recommendation of taking different routes when going to and returning from the Eid and Friday prayers, as well as other acts of worship. For example, a Muslim should leave from the right and return from the left. This is authentically reported to have been done by the Prophet (may Allah's peace and blessings be upon him) for the two Eid prayers. Jābir (may Allah be pleased with him) reported that, on the Day of Eid, the Prophet (may Allah's peace and blessings be upon him) used to go to the prayer using one route and return using another. The same is indicated in this Hadīth. The scholars have held various opinions about the wisdom of going to the prayer via one route and returning via another. The most well-known of these opinions are the following: 1. The purpose of the two routes is that the routes would be able to bear witness in the person's favor on the Day of Judgment, as the earth will bear witness to whatever evil or good was done over it. So, if a Muslim goes for prayer via one route and returns via another, the two routes will bear witness on the Day of Judgment that he performed the Eid prayer. 2. The two routes are recommended to show that it is the day of the rite of Eid by having the markets filled with crowds of people everywhere. When people spread out through the paths of the city it makes this rite obvious, and the Eid prayer is one of the rites of Islam. This is also proven by the fact that people are ordered to go out in the deserts to show that it is Eid and declare the rite. 3. The Prophet (may Allah's peace and blessings be upon him) used to go to the prayer by one way and return by another due to the needy who were to be found in the markets. So, he might find some of them on one way and find others on the other, and would be able to give to them all. The most sound opinion is that it is done to show that it is the day of the Eid prayer by having people going to it from all the roads of the city. As for Hajj, as reported in this Hadīth, the Prophet (may Allah's peace and blessings be upon him) took different routes when entering and leaving Makkah. He entered through its Higher Pass and left through the Lower Pass. He, may Allah's peace and blessings be upon him, did the same when he went to ‘Arafah, he took one route when he headed towards it and another when he left. The scholars also held different views as to whether the Prophet (may Allah's peace and blessings be upon him) did that as an act of worship or just because it was easier for him, i.e. that it was easier for him to enter through the Higher Pass and leave through the Lower Pass. The scholars who adopted the first point of view said that it is an act of Sunnah to enter Makkah through the Higher Pass and leave it through the Lower Pass. The same applies to ‘Arafah, according to them. Other scholars maintained that the matter depends upon the convenience of the route. So, one may take the way that is more convenient, no matter whether that is the Higher or the Lower Pass. Whatever the case, if a pilgrim of Hajj or ‘Umrah can easily enter Makkah through its Higher Pass and leave through its Lower Pass, that is a good thing, because, if it is an act of worship, he has done it, but if it is not, there is no blame on him for doing it. If he could not do that easily, he should not burden himself by this. In fact, now, all the routes to Makkah have been brought together in just one and Muslims should not disobey the orders of the Muslim ruler. Praise be to Allah, there is a choice in this matter.