Touch pad 'touch-click' not working but 'double-touch-scroll' working?

This also working for me:

synclient tapbutton1=1

If you do not have synclient in your distro (e.g. Kali), apt-get install xserver-xorg-input-synaptics, reboot, then try again. See this answer for a way to keep synaptics settings persistent between reboots.

But...

As Linux users, we usually trying to fix problems via terminal, digging in text files, and all similar complicate stuffs, but answer is much simpler this time :)

Kali Linux have an option for turn on/off "Tap to click", in /Settings/Mouse & Touchpad. This option is unchecked by default. All to need to do is check.

The issue has been resolved! Due to Gilles's helpful tip to check "xinput" settings, I have found I way to fix the single tap. First of I ran

apt-get install xinput

This installed xinput in the first place. Then I did a little digging and found my touch pad which had an ID of 14. I listed its properties with

xinput list props 14

I then found a property which was called "Tap Action". I noticed that its status was '0', so I checked out Synaptics's Online Manual (http://www.x.org/archive/X11R7.5/doc/man/man4/synaptics.4.html), and located the tap action thingy. To fix the problem I just had to execute

xinput set-prop 14 "Synaptics Tap Action" 1, 1, 1, 1, 1, 1, 1

I placed that into startup command so it'd run each time I logged in.