A crash report or something else would be welcome. Here we don't have much info to work on.

@Clément Foucault (fclem)
What do you want in that case? Would you like me to crash Blender again and then copy what the crash report has in a document?

Yep crash report could be a good start.

I was hoping you'd say that!

https://www.dropbox.com/s/i48vsjb8jnv45vg/Blender_Crash_Report.rtf?dl=0

How's this?

@Erik G. Riebling (E-ManAnimates) You can attach the file directly to your comment next time.

Well the crash is in the driver so it's related to drawing but that's quite vague as it crashes at context unbind at gpusSubmitDataBuffers.

Application Specific Signatures:Graphics hardware encountered an error and was reset: 0x00000000
Thread 0 Crashed:: Dispatch queue: com.apple.main­thread
0   libsystem_kernel.dylib        0x00007fff97e9cf06 __pthread_kill + 10
1   libsystem_pthread.dylib       0x00007fff897724ec pthread_kill + 90
2   libsystem_c.dylib             0x00007fff8a7cd77f __abort + 145
3   libsystem_c.dylib             0x00007fff8a7cd6ee abort + 144
4   libGPUSupportMercury.dylib    0x00007fff8d887e5c gpusGenerateCrashLog +158
5   com.apple.AMDRadeonX3000GLDriver0x000000011474022b 0x11471a000 +156203
6   libGPUSupportMercury.dylib    0x00007fff8d889361 gpusSubmitDataBuffers +511
7   com.apple.AMDRadeonX3000GLDriver0x000000011477da3d 0x11471a000 + 408125
8   org.blenderfoundation.blender 0x00000001058ab783 DRW_opengl_context_disable + 19
9   org.blenderfoundation.blender 0x0000000105265d71 wm_draw_update + 1873
10  org.blenderfoundation.blender 0x0000000105263b60 WM_main + 48
11  org.blenderfoundation.blender 0x000000010525fc66 main + 982
12  libdyld.dylib                 0x00007fff9879c5ad start + 1

That does not really help but that's better than nothing. I don't have the hardware to reproduce it so I can't investigate. Maybe @Arto Kitula (akitula) can investigate further.

Is this crash only limited to my current OS and hardware? If so, would updating my OS help resolve the crash?

Anyway, I looked into the problem again and tried hitting 1, 2, and 3 on my keyboard. I thought that the crash was limited to the UI, but even the keyboard shortcuts for selecting edges and faces are not exempt.

EDIT: After discussing it with my friends, it seems like the problem is that the GPU is not installed properly. While I don't know if this is 100% the case, it lines up well with the fact that I had my GPU replaced a couple of years ago. My assumption is that the people didn't install it perfectly, which leads to a few errors on my computer. They likely didn't notice it because my computer is still running well enough. In any case, I'll try fixing this problem next week.

Blender 2.8 CRASH on Switching to face select

iMac (27-inch, Mid 2010)
Mac OS X Yosemite, Version 10.13.6
2,8 GHz Intel Core i5
12 GB 1333 MHz DDR3
ATI Radeon HD 5750 1024 MB

Very interesting. It sounds like my problem isn't exclusive to me anymore. I recently upgraded my OS to Sierra, which seems to provide a huge performance boost; however, Blender still isn't fully working for me. If all else fails, I'll either obtain the High Sierra upgrade or just reinstall my OS. Also, gaining a new MacBook Pro is not out of the question.

By the way, can you provide us with a copy of the crash report?

Great! Let's hope the developers will get to the bottom of this with your information on the table.

By the way, I tested version 2.79.6 on my MacBook Pro yesterday. Unsurprisingly, the Edge and Face Select options work perfectly. Would that provide an additional clue to my dilemma?

UPDATE:
Since my family owns more than one computer, I downloaded Blender 2.8 on those systems. When I tried the iMac with Sierra from mid or late 2013, it ran Blender without a hitch; however, the iMac with High Sierra from mid 2011 suffered the same face and edge select glitch as my MacBook Pro. What I'm gathering is that the problem is the hardware inside the computer. If the Blender team would adjust the compatibility with Mac models from 2011, that would help me a great deal. Otherwise, obtaining a new computer is my best option right now.

System Information
MacOS High Sierra Version 10.13.2
iMac (27-inch, Mid 2011)
Processor 2.7 GHz Intel Core i5
Memory 16 BG 1333 MHz DDR3
Startup Disk Macintosh HD
Graphics AMD Radeon HD 6770M 512 MB
Serial Number C02FM2PEDHJP

UPDATE2:
I don't know how you guys managed this, but the latest build of Blender finally works on my computer!

Working version
Blender 2.8 Alpha 2 Date: 2018-10-13 21:55 Hash: 55e3c17ccc1 Branch: blender2.8

I will let you know if I run into any other problems, but I'm satisfied so far! Also, I hope this new build works for Jorge (JM).

By the way, if Jorge Rocha is reading this, it wasn't my intention to alert him of this thread. Instead, I was trying to inform Jorge (JM) that Bender probably works on his machine now. Please forgive me.