A visiting prophet stands firm against an offer of hospitality, driven by strict instructions that govern his mission. His refusal to accept the invitation stems from two separate restrictions placed upon him [מלבי״ם].
The first limitation dictates his route of travel. Accepting the offer and traveling to the host's home would force the prophet to retrace his steps and walk back along the exact same path he just took, an action he is expressly forbidden to do.
The second limitation is a complete ban on consuming food and drink. Beyond the issue of his travel route, the prophet is absolutely prohibited from ever sitting down for a meal in that specific location.