See if it was an aspiration and framed as such, I'd have no problem with what was said. Labour want to put an end to homelessness... Yup no problem, it's a perfectly correct thing to want to do, I'd believe them. But that wasn't what was said and they do this all the time and in this instance its pretty much impossible to do what they say they will. Saying they will end it and end it in the term of one parliament just will not happen, so I find it very hard to believe them.
The homelessness issue is sort of irrelevant to my point in a way. It's just a particular issue, out of many where Labour claim they will do the impossible and as usual, they don't tell you how they'll do it either.