Why did Israel reject Jesus when He came as their Messiah?

Israel rejected Jesus because in unbelief they would not reckon with the sin problem first. They wanted a ruling king and kingdom, not a redeeming Savior, and expected a conquering hero on a white steed. Instead He came on a donkey, which offended their expectations, so they rejected and crucified Him—though not all.

Les explains that Israel was seeking the King and the Kingdom, but they did not get what they were seeking. The reason was unbelief: they would not reckon the fact that they first had to deal with the sin problem. They needed a redeeming Savior, not just a ruling king, and that is why they did not want Him. Les gives the illustration that the ancient picture of a conquering hero was someone riding in on a big white steed, prancing like a show horse. Instead, Jesus came into Jerusalem on a donkey, and not even a grown one, which blew their minds. No king comes in on a donkey; they thought he should come on a great white stallion. So they rejected Him and crucified Him, but not all. The election obtained what Israel sought, while the rest were blinded, and today many in Israel remain spiritually blind.

Romans 11:7

What then? Israel hath not obtained that which he seeketh for; but the election hath obtained it, and the rest were blinded.

What happened to the rest of Israel that could not believe Jesus was the Christ?

Those in Israel who could not believe that Jesus was the Christ were blinded. Scripture says the majority rejected Him, while only a few recognized Him and became the elect. The Book declares that the rest were blinded, and this is not an accusation but what Scripture states.