Why must he be very man, and also perfectly righteous?

Because the justice of God requires that the same human nature which has sinned, should likewise make satisfaction for sin; (a) and one, who is himself a sinner, cannot satisfy for others. (b)

(a) Ezek.18:4 Behold, all souls are mine; as the soul of the father, so also the soul of the son is mine: the soul that sinneth, it shall die. Ezek.18:20 The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him. Rom.5:12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: Rom.5:15 But not as the offence, so also is the free gift. For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many. Rom.5:18 Therefore as by the offence of one judgment came upon all men to condemnation; even so by the righteousness of one the free gift came upon all men unto justification of life. 1 Cor.15:21 For since by man came death, by man came also the resurrection of the dead. Heb.2:14 Forasmuch then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil; Heb.2:15 And deliver them who through fear of death were all their lifetime subject to bondage. Heb.2:16 For verily he took not on him the nature of angels; but he took on him the seed of Abraham. 1 Pet.3:18 For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit: Isa.53:3 He is despised and rejected of men; a man of sorrows, and acquainted with grief: and we hid as it were our faces from him; he was despised, and we esteemed him not. Isa.53:4 Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted. Isa.53:5 But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed. Isa.53:10 Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the LORD shall prosper in his hand. Isa.53:11 He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities. (b) Heb.7:26 For such an high priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens; Heb.7:27 Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people's: for this he did once, when he offered up himself. Ps.49:7 None of them can by any means redeem his brother, nor give to God a ransom for him: Ps.49:8 (For the redemption of their soul is precious, and it ceaseth for ever:) 1 Pet.3:18 For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit.