UPS doesn't offer every service to every address. The most common case is a Ground/residential mismatch - the selected service isn't valid for that address type, so the order returns to Assign instead of getting a label ("service not available").
How to fix it:
Choose a UPS service that's valid for the destination (e.g. a residential-eligible service).
Confirm the address classification (residential vs. commercial) is correct in Shopify.
Watch for service restrictions like Saturday delivery to states that don't support it.