I can't get my 2560x1080 monitor to show its native resolution on my Mac
Your Mac has limits in the resolutions it can send to the monitor and the monitor has limits in the resolutions it can show from the Mac.
The monitor communicate with the Mac and sends it a list of predefined resolutions it wants to get. The Mac does or doesn’t activate each of these resolutions depending on its own capabilities.
For example, the monitor will send 1920x1080 at 60Hz as well as 2560x1080 at 60Hz as its wanted resolutions.
If 2560x1080 at 60Hz doesn’t fit the Mac’s capabilities, then the Mac will only activate 1920x1080 at 60Hz.
In this case, there's no other predefined resolution claimed by the monitor that fits inside the Mac's limits.
SwitchResX doesn't push these limits. SwitchResX helps creating resolutions within the Mac's limits.
One of the limitations of most Macs before 2014 when using a DisplayPort output is a resolution bandwidth of 165 MHz.
With SwitchResX, you could define new resolutions that fit inside the monitors and the Mac’s limits, but that are not natively claimed by the monitor.
Please note that defining 2560x1080 at 60Hz in SwitchResX is of no use: the Mac does already know that the monitor wants this resolution, but the Mac has refused to enable it. Defining it a second time will be useless: the Mac will refuse it again.
However, you can define 2560x1080 at 50Hz for example, which is a resolution that fits in the standard limitation of 165 MHz for the bandwidth. Most of the times, a good monitor can handle this lower frequency.
SwitchResX will help the Mac and the monitor into finding a resolution that matches their capabilities and is better than the only 1920x1080 resolution that you now have.
For this, you only have to define a custom resolution in SwitchResX with the parameters of the native resolution of the monitor (which you can get from the monitor’s EDID), and lower the frequency before saving the resolution (to 40Hz, for example).
Then save the settings and reboot when SwitchResX asks it. You can also try to create a custom resolution, checking SwitchResX "simplified settings" and selecting a formula like CVT-RB.
This will for example allow to define 2560x1080 in 50Hz which will stay under the 165 MHz limit.
After reboot, the resolution should be marked "active" and should be selectable in the SwitchResX menus.
If selecting the resolution does work, you can try again with a slightly different frequency (51, 52Hz, etc) until you face a limit.
If the resolution is marked "not activated" or "invalid", you should try other parameters by lowering the frequency, for example. This means the Mac doesn't accept the resolution.
If the resolution is "active", and if selecting the resolution brings a message on the monitor like « out of range » , that means that the Mac has accepted the resolution, but the monitor hasn't.
In this case, you can continue searching for a resolution that matches both limitations, but sometimes there will be none: in this last case, you’re out of luck.
If there's no resolution that fits in both your Mac and your monitor's limits, these limits have no common space. In this last case, this cannot be corrected by software.