If you want to simply state that you agree with her points, use the present tense. Adding forms of the past opens up various nuances. Perhaps these examples will be useful:
The Lord of the Rings is my favorite book.
I think so, too.
I have thought so, too, ever since I read it at age 12.
I thought so, too, until I read Kant's Critique of Pure Reason. [That's a joke, by the way.]
If you use the present perfect, you are tying your current understanding to a period of time beginning at some point in the past. If that point in the past isn't understood in the context, you need to supply it. This is why Tᴚoɯɐuo (that is one hard name to write) suggests that you say something like "all along" when you use it.
If you simply say This is what I have understood you are implying that you understand this now, and you have had that understanding over a period of time. You can leave that period of time unspecified, but you are conveying that that period of time exists.
There are situations where both present and past perfect have pretty much the same meaning, which is what makes the difference a bit difficult to understand. Suppose you say these:
This is what I understand from your explanation.
This is what I have understood from your explanation.
The reason that these have the same meaning is that in both cases, you get your understanding from the explanation. So, both mean that you understand this now, and both mean that you have gained your understanding from the period of time over which the explanation took place. That is implied in the sentence in the present tense, and specified in the sentence in the present perfect.