Door sweep install, why can't I make a hole in my metal door?
I think it's definitely your drill bits. I got a special bit for metal when I drilled a gigantic hole in our metal front door to install a viewing port. 

While you could install the kind of door sweep you're attempting to install, I'd suggest you go with an alternative. We installed this on the same door recently: http://www.homedepot.com/p/Frost-King-Slide-On-Door-Sweep-Stop-UDB77/203231840 It does not require holes, and as one formed piece that you slap on, you will be less likely to have issues with whether it's on straight, whether the screws or door holes strip, etc.

While it was hard to close/open the door for the first 1.5-2 weeks or so, it eventually broke in and has been working like a charm. Your door-threshold gap looks pretty tight though. Luckily many home improvement stores have generous return policies. We bought several types and screwed around until we decided which was likely to work best.