The real reason is that conservative ideology dictates that society will have winners and losers who end up in the correct spot in the heirarchy if society doesn't interfere with the natural sorting.
So it follows that homeless people don't deserve a "handout" or a leg-up just because they squandered their opportunities.
Leftists think that an ideology follows from a moral interrogation of the world as it should be, whereas reactionaries think the highest good is done by ensuring that people are in their correct spot in the heirarchy in relation to others; since some people are inevitably going to be homeless, there isn't much to be done about it and the leftists complaining about it are just virtue signaling to get votes.
Their justification is irrelevant once you realize the actual ideological reasoning.
Edit: I'm confused by the downvotes. Anyone want to tell me how I'm wrong? This isn't my ideology, but I think it's useful to understand your opposition on more than a cartoon-villain level, especially since they are so effective at selling their ideas to low-information voters.
Ah, that makes sense. Thanks!