I want to live in a place where you have to work to eat and must sink or swim. What would be a more strong motivator?
Most people agree, assuming the caveat for people who really do need help.
I want to have more than others and am willing to work for it. I also want to choose who I help that cannot fend for themselves.
That's fine, except that's an ineffective and unrealistic way to approach helping people. Ideally the choice could be left to everyone, but in a huge society like ours, such decisions are rarely able to be left to each individual. It just doesn't work.
If you really want a strong community, everyone needs to be productive if possible. I don't want to reward laziness or ignorance.
Nor does anyone else (well, at least 99.9% of people agree with you).
I want to see people who have more than I do. Otherwise how do you aspire to greatness?
Again, most people would agree.
To live in a community were everyone has the same house and car no matter how hard they work would be like living in a prison.
I'm not sure I'd go that far, but as usual, you seem to be arguing against strawmen here.
Most people want all the things you want: people who can work to do so and be productive, not helping people who don't need it, having different levels of wealth, etc. The main difference is in viewing how we achieve that stuff in a complex society like ours.
To get help to all those who truly need it, realistically we're going to end up helping people who don't need it. It's inevitable. We can do our best to minimize this, but generally the issue here isn't that some people are fine with helping people who are just lazy and some people don't like it. The issue is that some people exaggerate the magnitude of the problem of lazy people getting help, while others acknowledge that such a thing happens and should be minimized, but is also an inevitable by-product of helping the truly needy.
Some people recognize that extreme wealth inequality is a bad thing for society, but a certain level of it is good. The problem is that then other people interpret calls for lowering the inequality (but not getting rid of it completely) as calls for "everyone having the same house and car no matter how hard they work". Then the discussion ends up being dispelling strawmen, rather than discussing reasonable ideas for improving society.