Why circle an airport after takeoff? (SLC particularly)
I would assume it was to avoid terrain, traffic and/or the restricted airspace close to the airport, but there is at least one departure procedure from KSLC that calls for a climb in the hold. The SALT LAKE TWO departure includes this:


  Continue climb in TCH VORTAC holding pattern (hold south, left turn,
  341° inbound)


And several other departure procedures call for climbing right or left turns; combined with a few ATC vectors that could easily give the impression of circling.

You might try looking for the actual radar track online if you search flightaware.com or a similar site for your flight. That would let you see what track you really flew.