The point of the safety net in my opinion is to ensure equality of opportunity, not equality of ends. So you want to strive to ensure that children have an opportunity to learn and become productive members of society, in spite of the circumstances of their parents. You want to make sure that people who experience bad luck such as unplanned illness, economic downturns, natural disasters, etc. are not left totally destitute.
Or, turn it around: Why should you take the results of my work and give them to someone who won't (not can't) work? Why should someone who deliberately chooses not to try be considered entitled to me supporting them?
Someone who needs help? Sure, let's help them. Someone who just wants to be lazy? It's really unclear why they are more entitled to my money than I am.
A good social safety net means that poor people are not so busy trying to survive that they actually have the opportunity to improve their lot in life if they so choose. If you're not burning up 4 hours a day commuting and several hours a week washing clothes, you have more time to read to your children, or take some community college classes.
There will be people who decide that a life relying on the safety net is fine for them. Is that a worse thing than there being no safety net and people who have to drive to succeed are largely prevented from doing so? Or people who are working hard getting their lives destroyed due to one streak of bad luck?