We can be so busy trying to save our life that we fail to properly lose it. Jesus said we could not properly follow Him if we were continually preoccupied with our own comfort and security. A fully committed disciple of Jesus immediately obeys, regardless of the cost.
Losing our life does not mean we treat our life carelessly. It involves surrendering ourselves fully to Christ. We are His. He is free to do with us what He wants. He can spend our life in whatever way is most advantageous to His kingdom.
We have only one life to give to Christ. If it is held back, or overly protected, or driven by comfort, we may never know what we might have done, or become, if we had yielded ourselves fully to Christ.