God cares deeply for us. Seeing a person not take care of one's self doesn't bring God happiness. "Love others as you love yourself" implies that we should love ourselves. Christ coming to die for us, for our hope and overall/eternal happiness, is a big sign that we are valuable to God and should reflect that sort of thinking.
Some people may read this and think they are all set and love themselves the way God would like just fine, but the fact of how many people are overly busy, without time for much or any rest, would indicate otherwise.
There is such an emphasis in popular thinking these days on doing more, and not much about resting in God's grace, that people can become stressed easily. Stress can cause worry, frustration--all sorts of things that aren't helpful to that person or others.
God calls us to help others, out of a desire to bring him glory, but he also wants us to be humble and know our limits as humans. Limits mean we need sleep, lots of food, and time to just sit and reflect on truth and blessings. Jesus took time to be alone and rest at times. The Sabbath is a day a week God wants us to aim to rest.
For some people with families it's hard to make time, but planning ahead and thinking through ways to help get as much rest and taking care of one's self as much as possible is worth it.