Kill, yes. Harm? ... it depends heavily on the tree.



Running a thin rope with any weight in it could cause some damage to the tree, just by compressing the small tubes just under the bark that carry the sap up to feed the leaves. If you have a tree like a pine with a very thick bark, this is not much of a problem. But for trees like oaks or maples, this could cause some damage (especially if the tree is used a lot).



More importantly, a lot of campgrounds and areas will start noticing the cosmetic damage to the trees, even if the tree is not harmed, and start freaking out and banning hammock use on their lands.



Webbing is cheap, durable, and easy to use. It spreads out the pressure, minimizing damage to the tree.



I wrap my webbing around the tree a couple of times, then clip a carabiner to it. I have a drip ring on my hammock line that allows me to easily adjust the length of my hammock ropes. That way, putting up my hammock itself requires no knots whatsoever. Put up the straps, clip the hammock to the straps, use the drip ring slider to adjust the length of both hang lines, done. The carabiner and drip ring combine forces to drip all of the water off the line before it reaches my hammock. I've been out in torrential rain and stayed bone dry all night.



The rope ridgeline for my rainfly (550 paracord) is tied, but on the outside of the webbing.



Also, if you run a ridgeline all the way through your rainfly like I do, take a nut or washer or something, cut the ridgeline near where the rainfly starts on both ends, and tie the cut ends to either side of the nut/washer. The "break" in the line will allow water to drip off before proceeding under your rainfly and raining on you. Trust me, I learned that one the hard way. You can also just use the rainfly without a continuous ridgeline, but I like hanging small things under cover.