Basically, it is because God is Righteous and judges totally righteously, which means he cannot sweep sin under the carpet and dismiss it. Now, a capricious, man-made idea of a god predominates pagan religions. The Greeks had a pantheon of deities who would act on whim, generously bestowing favours, or with (very human) feelings of revenge or jealousy. Sinful humans who dreamed those gods and goddesses up, had those deities made in their own image, but with greater powers.
For instance, when you compare the flood legend of Gilgamesh (dated 1900 B.C.E.) with the biblical account (the event dated circa 2500) you see such differences. With Gilgamesh there's a 'Noah' figure instructed by the gods to make a boat to survive a flood, and to search for eternal life.
In the Gilgamesh story, no explanation is given for the flood, though in another Akkadian source (the Atrahasis Epic) the gods decide to destroy people because they are making too much noise! In the Epic of Gilgamesh the Noah-type character was Utnapishtim. Gilgamesh was a king and main character in the story who meets Utnapishtim. Gilgamesh never goes through the flood, only this character Utnapishtim does. Gilgamesh was supposedly part God and part man (as one of his parents was a god). It never says Utnapishtim was a God, though he does have eternal life in the story and helps Gilgamesh find the plant that gives eternal life at the bottom of the sea (which Gilgamesh loses on his way back to Uruk). But in Genesis, God sends the flood as a judgment on gross evil done by humans. Its recurring theme is that there is only one God. Unlike Babylonian gods, the God of Genesis is not afraid of the flood. He is in complete control of it. Nor does he deal with people in an arbitrary way. Saving Noah is as much the outcome of God's just nature as is the destruction of everyone else. This is a moral God, and his dealings with men and women depend solely on his own standards of justice and love, not on capricious self interest.
If you or I had any idea of the extent of the wicked depravity of humanity leading up to the flood, we would take the Genesis account seriously. Jesus did. He said that it is a warning for how things will be just before he returns. Now, back to the main point of the question - why God will not forgive sinners without sin being dealt with, God's way, which is by punishing his sinless Son, in our stead.
Protestants are agreed that all humanity is sinful and that sin alienates us from God, who is sinless. We cannot do anything that will remove our sin from ourselves. Only God can do that, as the account in Isaiah 6:1-8 shows:
"In the year that king Uzziah died I saw also the Lord sitting upon a
throne, high and lifted up, and his train filled the temple. And above
it stood the seraphims... 'Holy, holy, holy is the Lord of hosts; the
whole earth is full of his glory'... Then I said, 'Woe is me! for I am
undone because I am a man of unclean lips, and I dwell in the midst of
a people of unclean lips; for mine eyes have seen the King, the Lord
of hosts.' Then flew one of the seraphims unto me, having a live coal
in his hand, which he had taken with the tongs from off the altar: And
he laid it upon my mouth and said, 'Lo, this hath touched thy lips and
thine iniquity is taken away, and thy sin purged'." [Emphasis mine]
Although God is loving and forgiving, he cannot lovingly forgive sin by contradicting his own righteous law, that sin incurs a debt which, if not fully purged, will result in divine punishment. This would mean that all humanity would be doomed. So, God sent his only-begotten Son (who agreed to come) to be the one and only perfect sacrifice for sin the world has ever seen. Now all who trust in that one and only means for having the punishment for their sins borne by Christ instead of by themselves, can be pardoned legally. Justice has been seen to be done, at the cross. God's righteousness was demonstrated at the cross, for those with eyes of faith to see it and to trust in it.