That's right before he tells you to cut off your hand if it causes you to stumble. Either christians think Jesus is hyperbolizing, or lots and lots of men are doing a great job hiding a very serious injury.
In that spot, I believe he has a very valid point. But I don't see it the way you see it.
What Jesus points out is a stern warning against causing anyone to be tempted by your actions and stumble, by stating, it's better that you kill yourself than face judgment for causing anyone to stumble. He isn't advocating the act of suicide, but saying you will be judged harshly for causing someone to stumble, or even giving someone a license to sin through your words and actions.
For example, alcohol. A very hot issue with Christianity. I drink a beer on occasion. One with dinner, or one after a rough day at work to sooth my nerves. I don't drink to get drunk, just to relax, or enjoy a good beer. Even my fiance and I had a couple glasses of wine the night I proposed. Does that make me a sinner? It makes me as much of one as Paul advocating for Timothy to drink wine to sooth his stomach problems.
However, if this were a cause for stumbling, then I would have that weighing on me. Say if I drank in front of someone who is a recovering alcoholic? Or they even caught wind that I drink on occasion? And them, holding me in a position of respect, think "Well, if he can drink and still be a Christian, so can I!" But the problem with that person is that whereas I can stop after one, or two beers at the most, and be satisfied, and sober-minded, that person will more than likely not be able to.
It is the same situation. What if someone who is a recovering sex addict found out the OP is doing this, and respects the OP? "Well, if they can do this without having sex, so can I!" People place way too much trust in their own self-control, or their own Christian walk that they think that they are impervious to former triggers that could lead them back to their sinful life before believing Jesus and their repentance.
This has even put me on the fence of whether I should even continue drinking or not myself, since even word that I had a beer may reach the ears of someone who could stumble because of it.
I know this from experience. I am a recovering compulsive gambler. I don't remember much circa 2004-2007 save the times I was playing poker. I was on the path of recovery around September 2007. But I had a friend who was a Christian, but played poker occasionally. And I thought I could do the same.
In March 2008 I was on the verge of suicide after a bad run. And while I should've known better than to play in the first place, I have to pray that his causing me to stumble isn't held against him, because I was influenced by his ability to not let it effect him.