Why did Allah choose the months of the Dhul-Q'idah, Muharram, Dhul-Hijjah and Rajab as sacred months and not one of the other months?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Allah Says (what means): {Indeed, the number of months with Allah is twelve [lunar] months in the register of Allah [from] the day He created the heavens and the earth; of these, four are sacred. That is the correct religion, so do not wrong yourselves during them. And fight against the disbelievers collectively as they fight against you collectively. And know that Allah is with the righteous [who fear Him].} [Quran 9: 36]

The above verse proves that Allah Himself made the number of months twelve according to His eternal wisdom and determined that four months be Sacred; i.e., Thul-Qi'dah, Thul-Hijjah, Muharram and Rajab.

He made these four months worthy of reverence and gave them priority over others.

Allah chooses from the times, months and persons based on His Will and Knowledge and then orders His Slaves to respect that.

If it is said that all parts of time are alike and the question is asked why are some parts favored over others?

The answer is that all parts of time are not alike in the Sharee’ah. There are many examples that support this opinion. Don't you know that Allah honored al-Haraam (the precincts of the grand mosque in Makkah) more than any other place? He made Friday more sacred than other days of the week; He distinguished the Day of ‘Arafah especially for worship while the other days are not so; the month of Ramadan is distinguished by fasting and has more virtue than other months. Likewise, some parts of the day are designated for daily prayers; some nights are specified for particular worship such as Laylatul-Qadr (night of Decree). In addition, He chose some people as His Messengers.

All the above examples prove there is no reason for surprise that Allah made some months as sacred.

We conclude that doing good deeds in these sacred periods can have good results of purification, while the practice of bad deeds can have completely opposite effects. Thus, some scholars compiled their books during these times when supplications are answered. The Prophet was asked about which fast was more excellent, and he said: “The most excellent fast after fasting in the month of Ramadan is the fast in Allah’s month al-Muharram.” The Prophet also said: “Whoever fasts one day in the sacred month Allah will grant him the reward of thirty days for every day.” Many scholars establish the most severe Diyah (blood money) on the one who kills during these sacred months.

There are many other benefits derived from the sacredness of these months. Since human beings are inclined to evil, and to abandon it immediately is difficult, Allah designated certain times and places with a special degree of sacredness. A person's ability to abstain from evil is enhanced during these periods and in these places resulting in many benefits.

A) Abstaining from evil in such months is recommended, and thus bad deeds diminish during this period.

B) Refraining evil in such months develops the habit of hatred for it and consequently one becomes inclined increase his good deeds.

C) When a person practices good deeds during these months and gives up evil, it becomes harder for him to return to evil, and gradually he gives up all sins.

This is the wisdom behind the particular sacredness assigned to some places and times.
For more benefit, please refer to Fataawa 14951.

Allah knows best.