Companies like SpaceX and Blue Origin are rethinking the space industry. Private companies like these might put the first humans on Mars. You can read about what has changed in the past few decades in our timeline.
Money: If humankind does not explore and eventually inhabit other parts of the solar system, it will save a lot of money. For example, NASA’s (projected) budget for 2017 is $18,807,000,000 (almost $19 trillion). A lot of money goes into hiring employees, research, building, etc.
Safety: Space exploration puts many human lives in danger. Astronauts are at risk during missions, especially experimental missions. Something could go wrong, causing many deaths.
Other priorities: Not exploring the solar system can be a benefit because there are already other problems on Earth. We could focus the resources spent on space exploration on fixing those more important problems instead.
Knowledge: Failing to explore the solar system would result in less knowledge of space and our surroundings. So, if something were to happen in space that would endanger Earth (like an oncoming asteroid), we would be uninformed and unprepared for it.
Resources: Failing to explore the solar system may result in humans running out of resources on Earth and/or some kind of catastrophe without having anywhere to go. Also, other planets might offer resources that are rare/nonexistent on Earth; if we fail to explore the solar system, we will never get to use them.
Extinction: Another way failing to explore/inhabit the solar system can impact humankind is by causing extinction. Spreading out among other planets could help prevent all humankind from being wiped out all at once, should a disaster happen (such as an asteroid impact, climate change crisis, warfare, the sun engulfing the earth).