Vedanta is sometimes criticized for being too intellectual. But it could be argued that without using your intellect you are like a rudderless boat. And that's fine for most people not bothered by the karmic winds of time, but not for anyone who is serious about avoiding suffering and leading a peaceful life.
The intellect is like a muscle that needs to be frequently flexed in order to become strong and be put to good use. We first gain the right knowledge so that the intellect has something to work with, and then we use the intellect to apply the knowledge over and over again. When suffering arises—as it surely will—we employ the intellect to investigate, find the cause, and see how it measures up with what we already know about the truth of experience.
Suffering always occurs due to our lack of understanding and inability to discriminate between what is true and what is not. We might ask ourselves, where is the suffering coming from? Often, it involves the gunas (impersonal forces that influence our mental state) and our inability to manage them. Perhaps we just ingested (ate, drank, saw, heard, or felt) something we wish we hadn't, and now we feel very tamasic (depressed) or rajasic (anxious or paranoid). Or maybe it's the ego trying to pop its head up again, complaining about how it's always a victim and nothing good ever happens to it. When this occurs, it's time for the intellect to get to work with the tools it has been provided.
The individual might ask, "Am I really depressed or am I just out of balance and need to take better care of myself?" Or if the problem is the small self, "Is there really a victim here? Have I nothing to be grateful for?" Thus, the usual sequence is suffering, followed up with an inquiry (why am I suffering?), followed by a challenge (is my feeling sorry for myself justified?), followed by the application of knowledge (what do I know that applies to this situation?), followed by a resolution (the end of my suffering):
Suffering > inquiry > challenge > application of knowledge > resolution
For example, lets say today I wake up with a very strong feeling of lack due to an old samskara (deep psychological impression) that comes to visit me from time to time, telling me, as Vedanta teacher James Swartz puts it:
I’m a frightened needy little worm, munching my way through the experiential garbage heap of the world, looking for fulfillment. Life is tough and I am lonely, fearful, depressed and driven by my desires most of the time. You say I am fine but I don’t experience myself this way.
So, already we have the suffering, accompanied by a feeling of dread and perhaps, depression. Life, all of a sudden, feels very heavy. I have little or no motivation. I don't even want to get out of bed. I'm wading in the thick mud of tamoguna and I am now firmly seated in samsara.
Next, comes the inquiry: Who is suffering? Where is this suffering coming from? What initiated it?
Followed by the challenge: Is the suffering "me" or just an object known by me? Is my feeling hurt actually justified or is it just the small self complaining?
Followed by the application of knowledge: This feels like an old samskara that hasn't been totally put to rest. Anyway, I am not my likes or dislikes, nor am I the ego. I am the Self, that which is witness to all of this.
Lastly, the resolution: I am already whole, complete and unlimited as pure, infinite, non-dual awareness. My small self tells me I'm not okay, but Self-knowledge tells me I'm perfectly fine and will always be so. This suffering makes no sense and has no logical foundation.
Sometimes, it helps to investigate your suffering by writing it down. Writing gives you the ability to look at your problems from a 360˚perspective. Also, to resolve your problems, you first need to provide your intellect with the right knowledge. Many people have the wrong knowledge or are stubborn or unwilling to do the work to gain the right knowledge. But without the right tools you are always going to be limited to the degree at which you are able to resolve your problems.
In the end, Vedanta and Self-knowledge is hard and—yes—it is intellectual; that is, it requires a certain mental capacity, curiosity and ability to problem solve. But for some individuals, there is no alternative. You either gain the tools of right knowledge and apply them using the strength of your intellect, or you continue to suffer. Building a house is hard and also requires thinking skills, but that doesn't stop some from learning the carpentry, electrical and plumbing needed to do it. Nothing is free in life, but more than ever in the history of our species do we have so much wisdom knowledge available to us. All we need now, is the will.