Couldn't the resurrection be a legend that grew over time?

The evidence is against it. The claim appears in the earliest layers of the record, within a few years of the events, and was first proclaimed in Jerusalem itself, where the tomb could be checked. That is far too soon and too public for legend to replace memory.

Why does it matter that the disciples died for it?

People die for beliefs they hold sincerely, but the disciples claimed to have seen the risen Jesus themselves, so they knew whether it was true or a lie. Their willingness to suffer and die shows they were not knowingly spreading a hoax.

Who is Jesus?

Why do Christians believe Jesus rose?

Q: Why do Christians believe Jesus rose?

Because the earliest evidence points that way and nothing else explains it as well: the empty tomb, many people convinced they met Jesus alive, and terrified disciples suddenly willing to die for the claim. This conviction appears at the very start, in the city where he was killed, not as a later legend (Acts 1:3).

The short answer

Christians believe Jesus rose because the earliest evidence points that way and because nothing else explains it as well. The tomb was empty, many people were convinced they met Jesus alive, and terrified disciples were suddenly willing to suffer and die for the claim. This conviction did not grow slowly as a legend; it appears at the very start, in the city where he was killed, and it turned grieving followers into bold witnesses.

This is not blind belief handed down without reason. The first Christians gave an account of why they were sure, and it can still be examined today.

It began at once, not centuries later

The claim that Jesus rose appears in the earliest layers of the record, within a few years of the events, as a summary already being passed on. There was no time for legend to overwrite memory. And it was proclaimed first in Jerusalem, where anyone could have walked to the tomb and checked.

“To whom also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days.”
Acts 1:3

Changed people are hard to explain away

The disciples had scattered in fear when Jesus was arrested. Within weeks they were publicly declaring he was alive, undeterred by threats, prison, and death. People will die for a cause they believe in, but these witnesses claimed to have seen the risen Jesus with their own eyes; they were in a position to know whether it was a lie. A former persecutor, Paul, joined them after his own encounter.

It comes back to Jesus

In the end Christians believe Jesus rose because the risen Jesus met people and changed them, and has kept meeting people ever since. The invitation is not to take it secondhand but to look at the evidence and at him. Ask honestly whether anything but a real resurrection accounts for how it all began.

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Related question: Is the resurrection of Jesus real?
Related question: Is the empty tomb evidence?