Grudem (Systematic Theology, p541f) outlines a number of reasons.  What follows is based on his discussion.

1. To be our representative.  Jesus obeyed where Adam had failed to obey.  This is seen in the parallels between the time of testing in the garden, Gen 2:15-3:7, and Jesus’ time of temptation in the wilderness.  It is seen also in Paul’s comparison of Adam and Christ in Rom 5:18f; cf. 1 Cor 15:45,47.
2. To be our substitute.  Only a man (and not an angel, according to Heb 2:16f) could take the plan of a man.  And, indeed, he had to be a man like us in every way, except sin.
3. To be our mediator.  Because we are sinners, we need someone who can represent God to us, and us to God.  To fulfil that role, Christ had to be fully human as well as fully divine, 1 Tim 2:5.
4. To fulfil God’s original purpose for humankind to rule over creation.  It is clear that this was indeed God’s original purpose, and equally clear that we failed to fulfil that purpose.  God intended everything to be in subjection to man, but this intention has not yet been realised, Heb 2:8.  Christ entered our human race and through his perfect obedience has earned the right to rule over all things, Heb 2:8; cf. Mt 28:18; Eph 1:22; Rev 3:21.
5. To be our example.  It is only if Jesus is our fellow human being that he can be the model and pattern for our own humanness.  Thus, we are called to walk as he walked, 1 Jn 2:6, and indeed we will one day be ‘like him’.  We are being changed into his likeness, 2 Cor 3:18 and image, Rom 8:29.  Christ has left us an example of suffering, 1 Pet 2:21.  We are to look to Jesus, the pioneer and perfecter our our faith, Heb 12:2.  When he face hostility, we are to consider the hostility he face, Heb 12:3.  Paul’s goal was to become like him in his death, Phil 3:19.
6. To be the pattern for our redeemed bodies.  Jesus was raised as a man in order to be the first-born from the dead, Col 1:18.  His resurrection body, 1 Cor 15:42-45 is the firstfruits of our own, 1 Cor 15:23.
7. To sympathise with us as our High Priest.  Because he suffered and was tempted as a man, he is able to sympathise with and help those who are tempted, Heb 2:18; cf. Heb 4:15f.