Will I harm my car if I install a k&n filter?

I have a 2003 Honda Element 4 speed auto Awd. From the research of this filter, it claims to have more air flow and less restriction, therefore it is suppose to give better gas mileage and throttle response. However, if that's the case wouldn't that means it's actually capturing kore dust particles in compensating for better air flow. It other words, destroy your engine?

This claims don't seem to make sense to me.
How is that possible that it's better than OEM? Would their be a trade off for something else?

OEM filters are designed for maximum of everything
air flow, dust particle capture and air volume
You can have a filter that can catch .01 mincron dust but the air flow is affected
you can have an air filter that catches 1 mincron and the air flow and performance of good
you can have a filter that only catches 5 microns or bigger and you have good air flow but engine life is reduced
never fit any thing more in micron size than what is stipulated in the OEM filter specifications

K&N filters require the filter media to be treated with a light coating of oil, which can be sucked into the intake system and can contaminate sensors in the intake stream. "Lifetime" washable filters like the K&N were probably a good thing back in the days of carburetors, but not so much for cars with sensitive electronic fuel injection.

No, K&N filters are high quality.

It probably won't hurt it badly, although as JetDoc says the oil from it can cause trouble. However, it is impossible for it to improve fuel economy. In the days of carburetors restrictive air filters made the engine run richer, but with electronic fuel injection like your Honda Element has restriction just acts like the throttle is not open quite as far.

I'm not a fan of K&N filters.

Stick with the stock filter. K&N are trouble. I know from experience.

Not as much as you do driving it at 90-100 mph.