I'm learning at a beginner level. My current topic is to construct verbs using ません and ませ. In the example I was given "I will not be present at today's meeting" translated as:
今日{きょう}は、会議{かいぎ}には出{で}ません.
But my understanding of that sentence has the opposite meaning: "I will not skip today's meeting".
So my question is why (leave 出), is ending with ません instead of ませ?
Let's start by looking at 出る in a dictionary. As we scroll down the list, it might seem to you like the word somehow turns into its opposite: we have "to leave" and "to go out", but also "to come out", and then "to appear", and then somehow "to attend" and "to participate".
We need to think about these verbs a little more carefully in English, first. The ideas "leave" and "attend" are not opposites in English. The opposite of "leave" would be more like "remain". You might think, "if I attend the meeting, that means I'm not leaving the workplace". But this only makes sense because you're assuming that you're already at the place where the meeting will occur.
When you leave the house - or your office, or your cubicle at the office - it's likely in order to go to somewhere else. That destination is the に-marked part of 出る, and your starting point is the を-marked part.
The kanji 出 can be seen as formed from two copies of 山 (mountain); but more accurately it is a mountain with its central line extended into an "open box/mouth" 凵. (That's why 出 has only 5 strokes instead of 6.) The "story" I tell myself (I don't know how close this is to actual historical derivation) is that a river flows out from the mountains, into a basin.
If you 会議には出る, then you move yourself out from your current (unstated) position, to (に) the 会議, and this movement is furthermore a topic to emphasize with は (see also What is the difference between "に" and "には"?, は、には、に。。。what is the difference between them? etc.). In other words, you attend the meeting: regarding "to the meeting", you set out for it. And, of course, if you 会議には出ません, it's the opposite.
「〜に出る」 means "to attend" or "participate in". So it's simply saying, "I will not attend the meeting today." There's nothing special about it being 出ません.
Your translation would convey the normal meaning of 出る which, nontheless, requires a different case marker, を:
今日{きょう}は、会議{かいぎ}を出{で}ません
The second, equally important meaning is "appear/come forth/come out," and hence "participate", when expressing a location determiner. However, here another case marker must be used: に, as in your sentence
今日{きょう}は、会議{かいぎ}には出{で}ません
