I am trying to install a bike hoist in the ceiling of my garage. I found the ceiling joist using the stud finder and when I tried making a pilot hole, I noticed that I am hitting metal. I don't have full access of the garage crawl space but the location I went to has a metal spacer between the 2x4 and the drywall. Is it safe to drill through the metal spacer and into the 2x4 to install my bike hoist?
Update: From the photo provided, it doesn't appear to be a safety plate. I'm leaving this answer in case someone else comes here searching on metal behind their drywall.
If that's a steel safety plate you're hitting, then the answer is "no" you don't want to drill through it. It's installed to prevent accidentally nailing through the drywall, into the joists, and into some electrical or plumbing that's very close on the other side. Go 6" along the joist and try again, and if you hit wood instead of metal, thank the last person that was kind enough to install this plate.
When seeing the picture of the 2x4 hanger bracket at the end of the joist as shown I would like to comment that there is some concern with drilling through the bracket so that a screw or lag bolt can engage the hung 2x4. Screwing in too near to the end of the 2x4 could cause it to split and then the holding power of the screw would be greatly diminished. If you are using lag type bolts or larger sized screws carefully select the proper size pilot hole drill bit. This will help to keep the wood from splitting and give the strongest holding power. Afterall the last thing you want is for your hung item to come crashing down.