Why did Paul circumcise Timothy?

In his second missionary journey, Paul revisited the churches he had earlier established to strengthen the brethren and deliver the Jerusalem Council decisions to them. In his last visit to Lystra, Paul healed a crippled man from birth (Acts 14:8), causing a frenzy among the people to offer sacrifice to Barnabas and him. Later, jealous Jews stirred up the people to stone him and drag him out of the city (Acts 14:19). Was Lystra a total failure? Not quite! Today, we read of an encouraging situation in Lystra. Timothy joined Paul.
And he came also to Derbe and to Lystra. A disciple was there, named Timothy, the son of a Jewish woman who was a believer; but his father was a Greek.
He was well spoken of by the brethren at Lystra and Iconium (Acts 16:1-2).
From what we read in Acts 14 and here, we may conclude that despite the setbacks mentioned above, Paul managed set up a church in Lystra and this church was very healthy and active because from them came a saint of the Church, Timothy, a disciple μαθητής in Lystra, who was highly praised by the fellow believers (brethren) ἀδελφῶν in Lystra and Iconium of the Lycaonia region. Timothy travelled with Paul, learned from Paul and later became the head of the church in Ephesus. From a disciple, Timothy became a fellow worker (Romans 16:21), a true child in faith (1 Timothy 1:2), a beloved child (2 Timothy 1:2a) and a brother (Colossians 1:1). In the New Testament, the Church has collected two Pauline Epistles written to him.
In their journey, they visited the region of Phrygia, Galatia and Mysia but did not go to Asia and Bithynia. In enigmatic words, the Acts reports that the Holy Spirit (Spirit of Jesus) had prevented them from speaking in Asia and Bithynia. What does it mean? Did the people in Asia and Bithynia NOT deserve to hear the gospel, to receive salvation? Or did the Holy Spirit have some other plans in mind and the apostles would come back in the future?
When they came to Troas, two important things happened.
Firstly, Paul had a vision in which a Macedonian beckoned him to preach the gospel in Macedonia (Acts 16:9). Then, Luke joined the company.
And when he had seen the vision, immediately we sought to go on into Macedonia, concluding that God had called us to preach the gospel to them (Acts 16:10).
Here for the first time and until Paul & Silas were arrested in Philippi (Acts 16:19), we find the Acts written in the first person. Therefore, we conclude that Luke also took part in this section of the journey and elsewhere.
Now, let us go back to figure out why, given Paul's stance against circumcising Gentile believers, he circumcised Timothy. Wasn't such action self-defeating? In the letter to the Galatians, Paul prided himself for not circumcising Titus.
But even Titus, who was with me, was not compelled to be circumcised, though he was a Greek (Galatians 2:3).
Why was Timothy treated in a different way? Was it because Timothy was a half-Jew, while Titus a total-Greek?
Let us read again why Paul scolded Peter in Antioch (Galatians 2:11-14). Peter was influential. Others followed his examples. So, when Peter acted "insincerely" in the eyes of Paul, making others, including Barnabas, followed to act insincerely, Paul was furious and scolded Peter in these words.
If you, though a Jew, live like a Gentile and not like a Jew, how can you compel the Gentiles to live like Jews? (Galatians 2:14b).
Therefore, Paul scolded Peter for his "moral cowardice" and in setting a bad example. In his eyes, Peter did not have the guts to mix with Gentile brethrens in the presence of the circumcision party. Paul did not know the worries Peter had in his mind, not even when he wrote the epistle.
Now, can we scold Paul for circumcising Timothy out of moral cowardice?
A more mature Paul would later concede that in order not to disturb the conscience of weaker brethren, out of charity, he would refrain from eating meat offered to idols.
But if some one says to you, "This has been offered in sacrifice," then out of consideration for the man who informed you, and for conscience' sake -- I mean his conscience, not yours -- do not eat it." (1 Corinthians 10:28-29a)
So faith, hope, love abide, these three; but the greatest of these is love (1 Corinthians 13:13).
I don't know if Peter shared the same concern for the conscience of the circumcision party. This whole discussion of moral courage and conscience would be irrelevant because Paul had enough reason to circumcise Timothy because he was a half-Jew. Timothy should live like Jews and Paul. Perhaps, for the sake of convenience in their future missionary work in order not to attract unnecessary disruptions from hostile Jews, it was reasonable for Paul to circumcise Timothy and not Titus.

Dear Lord, life is really complicated. We have to make many moral choices in our daily life. May Your truth illuminate our conscience and strengthen our courage so that we may lead an upright life compatible to our Christian call. Amen.