It gets a little hard to "guess" the factors we're dealing with in this situation, but I'll try to help with the little experience I've had with ADB + Mac OS. The following are some questions that can help diagnose the problem; I will edit the answer according to future information:

Situation Checklist

(1) which version of Mac OS are you using? 10.6 (Snow Leopard), 10.7 (Lion), 10.8 (ML), 10.9 (Mavericks ) or 10.10 (Yosemite)? Or none of them? (Perhaps an older one.)
(2) did you mention Eclipse - I believe you have downloaded the latest Android SDK and have access to all the tools?
(3)when it says that "...I'm trying to enable debugger mode...", you are claiming that you have already unlocked the Developer Mode by quickly tapping (7-8 times ) on the Build number in "Settings > About the mobile " ? (Assuming the latest versions of Android, it may vary by manufacturer and version.).
(4) what version of OS do you have on your mobile? 4.1, 4.2, 4.3, 4.4? Is stock or did you load a custom ROM? If it is stock , have you taken access root?
(5) if we deal with a custom ROM , are you sure that it is working as it should ? I've had cases where, "zoei" so much the device, that I had to do a factory reset to get back to debugging as it should.
(6) Once all the above steps have been verified, you have come to test on another machine, preferably with another operating system (with its proper drivers installed.) like Linux or Windows ? Mac OS doesn'T need drivers to run ADB on most Androids (at least not the ones I tested - Samsungs Galaxy S2-S4, Moto E/G/X)

A little " Troubleshooting "

Now, let's try to deal with the problem.

ADB and privileges

The adb-server starts right the first time you run the ./adb devices command, as it needs a communication interface (e.g. "daemon") to hear itself on a random port and establish communication with the OS on the mobile. This daemon needs privileges to write via USB, and since it is a system based on UNIX, perhaps your problem may be that you are running adb from a location / user without privileges for both. Try running sudo ./adb devices to eliminate the possibility that it is a problem generated by lack of privileges. - If the daemon is already running, first of all, kills the process with a kill [PID]where [PID] is the process identifier. You can figure this out with something simple like ps aux | grep adb. (If by any chance the process hangs and does not "die", try kill -9 [PID].

Hardware > Software > environment Exchange

Another possible failure in this communication may, ironically, be the cable. Test with another USB cable to make sure this is not the problem. Or, in the same line, try to mount the USB sharing on your device and transfer some file via Android File Transfer, a client developed just for that - transfer files from Android to Mac. If you manage to do this transfer, then your cable and communication are OK .

If your hardware scan has no problems and there are no obvious reasons for the software not to "chat" properly, try the Step (6) from the checklist. Try it on another system and see if everything works fine. You can use something like 15 sec. ADB Installer to prepare a Windows machine in a matter of seconds to perform its test. Without having to download the whole SDK again.

If Android File Transfer, as mentioned above, works normally but adb keeps not seeing your device, you have one of two problems:
(1) your phone is not able to emulate USB debugging
(2) Your libraries/kexts in OS X are somehow messed up

In any case, it will only be possible to help in addition, with more information. I hope I could have helped in some way.