This is a common question for new photographers once they transition out of Auto mode, looking to improve their photography and learn more about their camera. When I started out, I was in auto mode and enjoying learning about taking photos. Once you get past this phase you begin to seek out new information on taking better pictures. For me this was a lot like when I learned to become a classical guitarist. I got my hands on everything I could listen to, read and play to make myself better.
I believe that learning the different modes, what do and the benefits each one has for a particular situation. Should you learn manual mode, yes, should you shoot in it all the time? There are many answers to this depending on who you talk to. Just as in anything, there are hard core camps that say absolutely and those that say no you should not.
I'm in the camp where I don't think you need to all the time. I do spend a lot of time in manual mode, but there are a lot of situations where I'm using the other modes depending on what I'm shooting. For example wildlife, most of the time I'm in shutter priority or manual. Shutter gives me the speed I need to ensue I freeze the motion if that's what I'm wanting. I recently was watching an interview with Moose Peterson who is an amazing wildlife photographer. Someone had asked him what mode he primarily shoots wildlife in and he answered aperture. Most people would have thought shutter or manual mode. I was surprised as well but Moose said he wanted to control the story he was trying to tell. He also stated that why would you spend all this money on a good camera with a great computer and then shut it off by putting it in manual mode.
On this I agree with him. If I know my subject isn't going to be moving around a whole lot, why wouldn't I put it in A priority mode? I'm composing the story I'm telling and if I'm metering the scene in manual mode, I have to start moving my aperture or my shutter speed and could miss my shot! Now on the flip side if I'm shooting an Osprey diving into the water to catch a fish am I going to keep it in aperture mode? No, I'm shooting in shutter priority so make sure I'm holding the speed I want to make that bird sharp to catch that action, freeze the bird and get a sharp image. If I'm watching two bear cubs laying in a meadow I want to separate them from the background and bring you into that moment and invoke an emotion that brings you into that story.
My suggestion is get out there, learn to shoot in manual mode and control your camera. Learn to how to get the proper exposure, what depth of field you want for your subject and how it effects your settings. Once you get a solid grasp on manual mode then work on the different modes available to you and figure out what works best for you and your work. You may find out you love manual and want to be in it all the time or use the other modes for how you want to tell the story. In the end, you have to do what works best for you, there is not wrong way. It's your story and you are telling it!