Because Jesus is only one who solved the problem of sin.
This is the core issue: How do we deal with sin? Other religions don't give the right answer. None of the leaders of any other religions-Buddha, Mohammed, Krishna, any of them-died for your sins. They had sins of their own to pay for.
Death is evidence of our sin. After all these years, with all our technology, the death rate is still 100%. But Jesus defeated death by rising from the dead. Death couldn't hold Him in the grave.
If you're unsure this is what the Bible teaches, think of Jesus in Gethsemane: "Father, if there is any other way of salvation, please let this cup pass from me" (paraphrase). But there was no other way, that's why Jesus' request was denied and He surrendered with, "Not my will, but Thine be done" (Luke 22:42).
"If righteousness comes through the law, then Christ died needlessly" (Galatians 2:21). We make a mistake when we simply tell people that if they don't believe in Jesus they're going to Hell. It's true as far as it goes, but it doesn't give an accurate sense of what's going on. A UCLA student once said to me, "Well, if your God is going to send me to Hell just because I won't believe in His Son, I don't want to spend eternity with a God like that." The biblical view, though, is not a narrow-minded, bigoted attempt on God's part to try to get people into Hell.
There's a better way to make the point more accurately. When I was speaking at a bookstore once, a lawyer came up to me and asked why Jesus was the only way. Instead of answering directly, I asked him a question: "Do you believe people who commit moral crimes ought to be punished?"
"Yes," he said.
"So do I," I responded.
Then I asked him, "Have you ever committed any moral crimes?"
"Yes," he said.
"So have I," I responded. "So now we have this difficult situation. We both believe those who commit moral crimes should be punished, and we both believe we've committed moral crimes. Do you know what I call that? Bad news."
I continued, "This is where Jesus comes in. We both know we're guilty, worthy of punishment. God offers a pardon on His terms: Jesus, because He has personally paid the penalty on our behalf. You can either take the pardon and go free, or leave it and pay for your own crimes yourself."
This approach gives an accurate sense of why the cross is important and why Jesus is actually necessary, showing God as merciful, not petty. The biblical message is not if you don't believe in Jesus you go to Hell. Rather the message is, "If you don't receive a pardon for your crimes, you'll be punished as you should be." The former approach confuses the doctor with the disease. If you refuse the doctor's medicine for your disease, the blame belongs to the disease, not the doctor. The obituary doesn't read, "Cause of Death: He didn't go to the doctor."
It's the disease-sin-that kills, not the lack of a doctor. Jesus is the only way because He is the only one that provides the cure for what ails us.