All the videos I've seen that use an angle grinder to sharpen a blade have the disc spinning into the sharp end of the metal.
Doesn't this mean that the disc could catch on the metal edge?

 

If you're not careful, sure. You don't attack the edge with the grinder, you gently move it across, keeping the blade cool to prevent losing temper.

 

The recommend method to sharpen a lawnmower blade is a hand file.

 

With lots of dings can you not also run the grinder at 90 degrees to remove material.
Why run the grinder into the edge to sharpen? Why not run it with the edge so it can't catch on it?

 

IMO a hand file is too slow ..... or maybe I'm just lazy

I either use a my 4.5" grinder or my bench grinder. The bench grinder gives better control but the 4.5" grinder is quicker. It is important to take the same amount of metal off of each side so the blade stays balanced! On nicked up blades where a good bit of metal has to be removed I'll hang the sharpened blade on a nail to check the balance and remove more metal on the heavy side until it's even. Not a high tech way of balancing but it's worked for me for over 40 yrs.

 

To answer your question, grinding from the leading edge keeps the grinder from feathering the edge of the blade backwards. You can try it and see, but sharpening from the cut edge will work best.

 

Hmm
This site says away from the edge. Guess it doesn't matter?

Orient the work so the wheel spins away from, not into, sharp edges. Wheels, especially wire wheels, can catch on an edge and throw the work piece or cause the grinder to kick back (Photo 1).

Number 7
How to Use an Angle Grinder | The Family Handyman

 

Nothing should be allowed to be thrown. There are exceptions to anything, but, in general, when using a power tool, either the tool or the piece is fixed. That's why, for example, inverted trash cans don't make good table saw stands. So the first thing you need to do is address that. I have used both bench and hand held grinders, and prefer hand held, mainly because it's easier for me, may vary for you, to see what I'm doing. If you use a bench grinder, as Mark mentioned, the tool is fixed, so you make sure to have a good grip and good control on the blade before engaging it with the wheel. If you are using a hand held grinder, the piece needs to be fixed. You can put it in a vise or clamp it to something. Because I like to weld, grind, etc. outdoors when possible, I often clamp my blades to a saw horse. As for direction, I sharpen from the cutting edge in, just like sharpening a knife, but you found contrary advice, so go with whichever way works best for you. If the blades need a lot of work, don't try to take it all at once. Attack it slowly, so that you don't end up taking too much at one time, and to minimize heat.

 

I've sharpened blades with a bench grinder. So much so that little blade is left (back in the days when I was cheap). But it's sharp and it cuts. But as I said earlier the recommended method is with a hand file. If the blade is so nicked up that a machine grinder is needed, then it should be scrapped and a new blade installed.

 

..... but some of us are still cheap :