The short answer
Cross-chain routes depend on live variables such as gas prices, liquidity, token prices, bridge capacity and provider availability. Any of these can change the ranking of available paths.

Why the best cross-chain route can change from one moment to the next.
Cross-chain routes depend on live variables such as gas prices, liquidity, token prices, bridge capacity and provider availability. Any of these can change the ranking of available paths.
A route can disappear when liquidity falls below a required level or when a provider temporarily stops supporting a network. Another route may become cheaper when market depth or gas conditions improve.
Because quotes are dynamic, users should not treat a route shown earlier as guaranteed. Re-request the quote when you are ready to sign.
Review the final output, fees and transaction sequence each time. This is especially important for larger transfers where small pricing differences can become meaningful.