Your Question

I’m still not sure how I can be angry and be the witness. Being angry feels all encompassing and being the witness feels stoic. Aren’t these polar opposites?

This is just the right question! Let me take some time to slowly go through your puzzle.

I. A Phenomenal Analogy

To illustrate what the witness teaching (which is a subset of the awareness teaching of Advaita Vedanta) says, let me employ a phenomenal analogy. The latter is a teaching tool whose point is to really highlight some specific aspect of the teaching. Therefore, care needs to be taken both with regard to the selection of such an analogy and with regard to how–in particular–the analogy is to be applied. 

Here’s the analogy I have in mind:

Let’s suppose that you own a single-family house, and let’s suppose that the shut-off valve for the water is located just outside of the house. Let’s suppose, further, that for as long as you can remember, no water has been flowing through the pipes in your house. One day a neighbor tells you that you can turn on the valve and, as a result, water will flow through the pipes, through the tap, through the shower head, into the washing machine, and so on. This neighbor, who is also wise, recommends turning the valve on to about 5-10%–that is, not on “full blast.”

You do as you’re instructed. In fact, you turn on the water to 5-10% and then stand back and watch as the water starts to slowly trickle through the pipes. Let’s say that you have X-ray vision such that you can see the water flowing gently through the pipes. Let’s say that you can also hear the water as it rambles along. And let’s say, finally, that you can somehow “feel what it’s like” for water to be flowing through this intricate system. 

Now, how does this analogy apply to the witness teaching?

II. The Witness Teaching And This Analogy

In this analogy, “turning on the water” is like letting (e.g.) any emotion appear. The emotion arises and flows (through energy channels of all sorts) of its own accord.

The witness is like the one who “stands back” in the above analogy. The witness is noticing various qualities that the emotion is undergoing. And yet, obviously the witness is not the house and therefore the witness is not involved in the course that the emotion is taking. 

III. The Witness Teaching: Philosophical Remarks

To get more of an experiential grip on what I’m about to say, you can refer back to I. and II. as many times as you need to. Now we turn to a philosophical treatment of the witness teaching.

1. The following are equivalent and thus shall be used interchangeably during the course of our conversations and meditations: namely, object, appearance, and arising. 
2. An object, appearance, or arising appears and then disappears. (There are other qualities too, but this characterization suffices for the purposes of this particular discussion).
3. Notice that all perceptions (sights, sounds, touches, flavors, and textures), all sensations (e.g., tingles, pains, involuntary spasms, etc.), and all of mind (thoughts, feelings, and desires) are objects. Please note that mind is also an object. Therefore, all of those just mentioned, including but not only mind-arising, appear and then disappear.
4. What is not an object is witnessing awareness.
5. Then what is witnessing awareness? The latter is that to which all objects appear. Said differently, witnessing awareness is the open background to which all “foreground” objects appear. 
6. Not being an object, witnessing awareness is not itself colored, changed, modified, harmed, hurt, or in any way affected by any object. That is, the appearance of, say, any emotion, including a strong one like anger, does not affect witnessing awareness. Nor does the disappearance of any emotion affect witnessing awareness. Metaphorically speaking, it remains “untouched.”
7. How are we to put all this together? The full experiencing of any emotion, or thought, or pain, or sensation, or whatever is made possible by the open background, which is witnessing awareness. This full experiencing is an appearance that’s appearing to this open, transparent, welcoming background. The full gamut of the object is experienced while the changeless, open, luminous, welcoming background remains unchanged. 
8. To speak very emphatically: there is no paradox in 7. Some, if they wished to speak in Western language, would call this last point (7) “healing.” Others might call it “the process by which catharsis occurs.” Others might call it inner purification (tattwa shuddhi). Suffice it to say, many different traditions and modalities give it many different names, but only the witnessing teaching properly and very rigorously thematizes “the setup,” setting out with supreme clarity “what the setup is” and also “how it works.”

IV. Answering Your Question

I’m still not sure how I can be angry and be the witness. Being angry feels all encompassing and being the witness feels stoic. Aren’t these polar opposites?

That’s because you can’t! You can’t, as it were, stand at “two different levels” at once!

1. Anger, sensu stricto, is allowed to arise. Since it’s common for Westerners, particularly men, to experience a good deal of “emotional constipation,” just try to “ease out” a small bit of anger. Say, ~5-10%. See clearly that anger, being an emotion, is an appearance, an appearance that is “not you” but that is illuminated by you, witnessing awareness.

2. Meanwhile, who’s letting anger arise at 5-10% intensity? You, witnessing awareness, are! YOU’RE PRECISELY THAT WHICH LETS ANGER (ETC.) ARISE IN THE FIRST PLACE!

3. Your dilemma thereby dissolves. (a) Anger is only “all-encompassing” when you take your stand as that ego-one who is allegedly experiencing anger “from the inside.” Yet that’s not where I’m inviting you to take your stand. I’m inviting you to stand, as ever, as witnessing awareness–and then let the emotion trickle out (or, in due course, surge through the pipes).

4. (b) The witness is neither stoical nor unstoical. It’s wide openness–like the vast Western sky. It’s (see this clearly right now–or go back to Section III. above) not a mental state, since the latter is another appearance. 

5. True, what you describe is a bit like the discovery of polar opposites: emotions, being sine-curve-like, are vritti (“streams,” “vibrations,” “modulations”) whereas witnessing awareness is beyond all sine and cosine curves. It’s just not “in play,” not “in the fray.” A better metaphor would be to say that all objects are “on the same, lower plane” while witnessing awareness is located–alone–on a higher plane. 

6. One last phenomenal analogy for now: suppose that you are like an open space, one that’s free of clutter (desks, chairs, tables, etc.). Suppose furniture is brought into you. Are you changed by the introduction of chairs? Nope, you’re still open space! Are you changed by the absence of objects? Nope, you’re still empty space. Witnessing awareness is like this.