Which will wear longer, a single chainring with 11-speed cassette, or triple chainring with 8-speed cassette? I am thinking of replacing the latter with the former. Someone said that the chain having to stretch 11 different ways would wear down the drive train faster. I think that the chain will last longer if it's not being thrown around at both ends. Who's right?
To all practical purposes, neither person is right. 

Even if cross chaining wears out drive lines (highly debated), 1x11 cannot cross as much as 3x8. A correctly choose chain ring on a 1x11 means you will normally be in a mid rear cog, so in normal riding, very little cross chaining would occur. If you ride extremely hilly country, and often sit in very high or very low gears, then you will probably still have a similar chain angle to a 3x setup most of the time.    

Chain wear and lifetime of drive chain comes down to a combination of regular maintenance, how much and in what way a bike is used. Within measurable parameters, a 1x11 will not wear out faster or slower than a 3x8. Over a large number of samples there might (although I have doubts) be a very small but statistically significant difference. 

Why are you worried about wear. A 3x8 speed drive train is much cheaper than a 1x11, so replacement is cheaper. 

There are valid reasons to go 1x11, and valid reasons not to, but wear is not one of them.