However, I will address this issue anyway, so that Christian missionaries do not assume that we are running away from this issue (although this issue poses no problem at all). This is because the hadith do indicate that the Prophet (peace be upon him) gave the order for the verse to be abrogated either by recitation, by ruling, or both. So if we want to accept these hadith then we have to accept them in their totality and conclude that abrogation is indeed a part of Islamic teachings.
One may ask, "What is the wisdom behind abrogating the ruling of a verse but keeping its recitation?" Suyuti answers this question:



فإن قلت‏:‏ ما الحكمة في رفع الحكم وبقاء التلاوة؟ فالجواب من وجهين‏:


‏ أحدهما‏:‏ أَنَّ القرآن كما يتلى ليعرف الحُكْم منه والعمل به، فيتلى لكونه كلام الله فيثاب عليه، فتركت التلاوة لهذه الحكمة‏. ‏

والثاني‏:‏ أنَّ النسخ غالبًا يكون للتخفيف، فأُبقيت التلاوة تذكيرًا للنعمة، ورفع المشقَّة



If you said: What is the wisdom of lifting the injunction but keeping the recitation? The answer is from two angles: -

One of them: The Quran is recited in order to know what injunctions it imposes and to act upon them, so it is recited because it is the word of Allah so he gets rewarded, so its recitation has remained for this wisdom.

And the second: That the abrogation is usually done to be an ease, so the recitation has remained as a reminder of the blessing, and removal of burden.

(Al Suyuti, Al Itqaan Fi Ulum Al Quran, Section: The Wisdom of the Lifting of the Injunction But Remaining of Recitation, Source: http://www.altafsir.net/)



So as we can see there are two possibilities. One is that we realize the blessing of Allah when we see that He relieved us from following a certain law and secondly we receive reward for reciting each verse of the Quran. This is confirmed in the following hadith:


It is well known that reading one letter of the book of Allaah brings a tenfold reward, as al-Tirmidhi (2910) narrated that 'Abd-Allaah ibn Mas'ood (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: "Whoever reads one letter of the Book of Allaah will have one hasanah for it, and each hasanah is a tenfold reward. I do not say that alif-laam-meem is a letter, rather alif is a letter, laam is a letter and meem is a letter." (Classed as saheeh by al-Albaani in Saheeh al-Tirmidhi, cited here)



So this way, Allah is giving us more Quranic verses to read and therefore we have a greater opportunity to receive a greater reward.
A third reason for the wisdom is like the example of the prohibition of alcohol. When we read the Quran we can see the wisdom of how Islam came to gradually change the people. We should also learn how to implement this in our lives and not to try to change over a day's time and to change ourselves gradually. We can see this wisdom by reading these verses from the Quran today and see that the Quran was revealed with wisdom.
Other reasons are that it is Allah testing those who claim to believe to also believe in what He changes of the Quran, which is His word. This is to make us feel humble by making us realize that nothing is in our hands and to praise the believers of before who adhered to the change without hesitation. This is also to let us know that the believers accept everything from Allah and that we had generations before us who fully supported the revelation.

One may also ask, "What is the wisdom behind abrogating the recitation of a verse but upholding its injunction?" (e.g. verse on stoning)
This is because the Sunnah is just like the Quran in that both are revelations and equal in authority (not in holiness). The Sunnah is also the actual law and this being a test to those who claim to believe in Allah; they must believe in the Sunnah too and that it takes place of the Quran in many areas. See here for proof of the necessity following Sunnah.
Finally one may also ask, what is the wisdom behind abrogating both the recitation and injunction of a Quranic verse? (e.g. verse on ten sucklings)

Allah has decided from the beginning that it is only good for the early generation of Muslims to receive this Quranic command and was not meant to be a permanent ruling for all Muslim generations to come.

Basically it was better for those people at that time and for certain individuals with strong faith but not as a race of people. Their test was different because God said He would bring something better:


Surah 2:106

None of Our revelations do We abrogate or cause to be forgotten, but We substitute something better or similar: Knowest thou not that God Hath power over all things?



So basically the verses whose recitation and injunction have both been abrogated have been made to be forgotten. So God with his wisdom knows that He would be able to substitute something like it or something better than it for certain different people.