Is it wrong to kill bugs?
Kill the right bugs
It depends on the bugs and how you kill them. If you are dealing with pests that have invaded your favorite plant I would say that you may want to take an approach that kills all of the bugs on that plant. A soap product is a good choice since they kill on contact but are biodegradable and only kill bugs that they are actually sprayed on.
In the broad sense; killing all bugs isn't such a good idea. Many bugs are our friends. They kill bad bugs; they pollinate our fruits and vegetables and some, like lightning bugs, just amuse us.
So while it would be nice to be rid of all of the mosquitoes, fleas, ticks and the like; a world without bugs wouldn't really work.
From a moral standpoint I don't believe it is right to kill something / anything simply because we can. In the grand scheme of things poisonous snakes, spiders, creepy crawlies all have that basic right to live and they are actually beneficial to us. We may choose to relocate them for our own safety but we shouldn't kill them unless it is necessary.
Likewise we may need to control bugs; and with bugs it isn't really practical to relocate them. Farms need to control bugs to keep us supplied with food and, unfortunately, there is no non-lethal way to do this. But when they can they should use approaches that only target specific pests. So go ahead and spray that cockroach but leave the Praying Mantis alone and she will kill that cockroach for you.