tl;dr The Space Shuttle mission numbers were assigned in numerical order of their planned launch sequence.<sup>1</sup> When that sequence changed, the mission numbers were not changed.

The question asserts

>  - it can't be the case that missions have been postponed so that    another mission came first either
>  - The Shuttle missions weren't postponed that much that another mission    came before
>  - Following the Columbia tragedy, they made it so that if a Shuttle    mission was postponed all subsequent missions were postponed too

Let's judge the validity of these assertions by examining the schedule history of a few missions.

**STS-114**

 - Baselined OV-104 Atlantis as ULF-1 Crew Rotation flight with launch
   date of 1/16/03 on 12/6/01
 - Postponed launch date to NET 3/1/03 on 9/16/02. Postponement caused by Engine Flowliner cracks.
 - Subsequent postponements after STS-107 Accident to NET 7/21/03, NET
   10/1/03, NET 12/18/03, NET 3/11/04, NET 9/12/04
 - Postponed launch date to NET 3/6/05 on 3/22/04. Changed flight to ISS
   Logistics Flight LF-1, canceled crew rotation, and changed orbiters to Discovery OV-103.
 - Postponed launch date to NET 5/12/05, 5/15/05, 5/22/05, 7/13/05
 - Rolled back from pad 39B to VAB on 5/26/05
 - Rolled out to Pad 39B on 06/15/05 and set launch date of 07/13/05 on 05/22/05.

**STS-121**

 - Baselined OV-103 launch date of 11/15/04 on 10/26/03
 - Postponed launch date to NET 5/5/05 on 3/26/04. Slip due to
Columbia accident
 - Postponed launch date to NET 7/10/05 on 10/29/04. Slip due to
Columbia accident
 - Postponed launch date to NET 7/12/05 on 2/17/05 to provide on
acceptable launch lighting conditions
 - Postponed launch date to NET 9/9/05 on 5/23/05 to reflect latest
planning decisions
 - Postponed launch date to TBD on 11/15/05
 - Postponed launch date to 5/10/06 on 3/16/06
 - Postponed launch date to 7/1/06

**STS-115**

 - Baselined OV-104 launch date of 4/10/03 on 3/7/02
 - Postponed launch date to 5/23/03 on 10/8/02; delays due to
engine crack repairs
 - Postponed launch date to NET 8/21/03 on 3/13/03
 - Postponed launch date to NET 10/30/03 on 4/17/03
 - Postponed launch date to NET 1/22/04 on 5/28/03
 - Postponed launch date to NET 7/24/04 on 7/29/03
 - Postponed launch date to NET 2/10/05 on 10/3/03
 - Postponed launch date to NET 8/28/05 on 3/22/04
 - Postponed launch date to NET 12/8/05 on 10/29/04
 - Postponed launch date to NET 2/16/06 on 5/23/04
 - Postponed launch date to NET 7/1/06 on 10/31/05
 - Changed launch date to TBD on 11/15/05
 - Changed launch date to NET 8/28/06 on 3/16/06
 - Changed launch date to NET 8/28/06 on 3/16/06
 - Advanced launch to 8/27/06 on 8/3/06 (actual launch date was
9/9/06)

**STS-125**

 - Added STS-125 to FDRD - launch date of 08/07/08
on 06/29/07.
 - Ppd. to 08/28/08 on 02/14/08. Slip due to ECO
sensor problems experienced during December
launch attempt of STS-122.
 - Ppd. to 10/08/08 on 05/27/08. Slip due to delays in delivery of ET
   127 & ET-129 (STS-400).

 - Ppd. to 10/10/08 on 09/08/08. Slip due to Hurricane
Faye impacts to HST payload readiness.
 - Ppd. to 10/14/08 on 09/24/08. Slip due primarily to
training time lost in the aftermath of Hurricane Ike.

 - Ppd. to NET Mid-Feb 2009 on 10/02/08. Slip due to
HST on-orbit failure of A-side of Control Unit Science
Data Formatter.
 - Ppd. to NET Mid-May 2009 on 10/30/08. Slip due to
checkout problems with HST spare control unit.
 - Selected May 12, 2009 launch date on 12/04/08.
 - Advanced from 05/12/09 to 05/11/09 on 05/01/09.
Advancing one day provided a 3rd launch opportunity
before range conflicts.


Data from [Space Shuttle Missions Summary][1]. 

I urge you to read the POSTPONEMENTS block for each mission you are interested in.  Postponements are changes to the *scheduled launch date*, scrubs are slips *after the scheduled launch date*.

Other questions of interest about shuttle launch scheduling and nomenclature:


https://space.stackexchange.com/q/41400/6944

https://space.stackexchange.com/q/37188/6944


<sup>1</sup> Before and after the goofy "let's hide our launch scheduling issues by obfuscation" era, that is

  [1]: https://spaceflight.nasa.gov/outreach/SignificantIncidents/assets/space-shuttle-missions-summary.pdf