CC2540 won't pair?

I am new to Arduino (only having been exposed to it for the last two months) I am using a CC2540 wireless BLE module to control a micro servo motor from an android phone as part of a project. However, whenever I try to pair the BLE module to my android, it's either not found, or if it is, it rejects pairing. I realize that there has been a question like this before, with the answer being that "the Bluetooth model is wrong", but I can't seem to figure out what that means even after looking it up multiple times.

To clarify:
-Nothing seems to be wrong with my code (also I am using Arduino UNO if that matters)
-GND is connected directly to Arduino UNO GND, VCC to 3.3v, Tx to pin 0, Rx to pin 1, the pins farthest to the left and right are not connected to anything
-As for the micro servo, red wire is connected to 5v, signal wire is connected to pin 13 and black wire is connected to GND.
-The module has a slow, blinking red light when it is powered.
-I tried the BLE scanner, which is able to find the device and "connect" to it (to which the red light becomes solid and not blinking anymore), but I don't really know what to make of that. I still am not able to pair it to my phone and use applications to control the micro servo.
-The message that appears is "BT05 pairing rejected"

I really just don't know what to do anymore. Any advice on where I might have gone wrong?

You do not need to pair your device with your phone. You can just connect to it. Pairing is optional for security features.

I suspect your library does not even support pairing. It requires the exchange and storage of keys. Because you are a hobbyist there is no need to ensure nobody connects to your application and reads out data. That is different for commercial products. There you have legal concerns like privacy of your heart rate and so on. So, implementing pairing is likely not adding a lot of value for open source libraries. I am not saying it’s not available somewhere, but I would not be surprised if it is not.

Your BLE scanner can connect to your Arduino. Try to read and write some values with the app. Once you are connected see what services are available and whether they are read and writable.