You say to another "get dressed" (1. You say this when someone asks you what you are doing? "I am getting dressed.")
But in the same way, why can't we say "get crossed" (crossing a street)?
Edit: Sorry, but this question is about: a person getting crossed vs. a person getting dressed.
You are exploring a parallel between "dress" and "cross": After one dresses, one is dressed. After one crosses (a street), is one "crossed"? The answer is no.
When one is finished dressing, one is dressed. "Dressed" is a state that one takes on after dressing, the state of wearing clothes. We can check whether a person is in this state by looking at him or her and noting whether we can see clothes or a naked body.
When one is finished crossing a street, one has not changed state, but location. There is no state of a person being "crossed" (at least with respect to this meaning of "cross" -- see footnote). Looking at a person, it is impossible to tell whether the person has crossed any given street.
Another possible explanation for this difference is that dress is intransitive -- it does not take an object -- or reflexive (I am dressing myself). Cross, on the other hand, is transitive. Its object, in the example, is the street.
(footnote: It is possible to say that a person is "crossed" when we use the sense of "to cross" that means "to oppose." A famous example is Shakespeare's "star-crossed lovers," Romeo and Juliet. Another common phrase is "double-crossed" as in "the criminals were double-crossed by their associate.")
You can say the street is getting crossed, but that sounds unnatural because it sounds like the street is doing something.
I think it would be grammatically correct to say that the street is "getting crossed" when someone is currently crossing it, although it would be better to say that it is "being crossed".
A Street Being Crossed vs A Person Getting Dressed
I think the difference, when compared to getting dressed, is that being 'dressed' is a persistent state. Once I am dressed, I stay dressed until I undress. How does a street become 'uncrossed'? Instead, the street is either being crossed right now, or it isn't. It won't stay 'crossed' after someone crosses it. I mean, technically it is a street that has been crossed, and therefore could be describe as 'crossed' forevermore, but that's not a useful concept.
Once again, compare this to getting dressed. You could say that one is "being dressed", but that means that clothes are currently being placed upon them, not that they have had clothes on for some time and still do. For that persistent state, or condition, we say that they "are dressed". In the process of "being dressed", they "got dressed", and now "are dressed".
Crossing a Person
To cross a person means to upset them. If someone stole my red stapler, you could say that they crossed me. One would not however say "I am crossed". One would say that "I have been crossed" and that "I am cross". This is another situation, rather than a condition, so we don't usually use 'get' here either. In other words, one would not normally say "when I get crossed", but instead "when I am crossed".
Other Examples of "get [verb]-ed"
Get tattooed.
Get ripped.
Get injured.
Get drunk.
In all of these, "get" means "become".
Getting dressed is a reflexive action which can be reworded as I am dressing myself. In other words, the person is acting upon himself, putting clothes on his own body.
Since the street is not part of the person's body, the phrase I am getting crossed makes little sense. It has nothing to do with crossing a street, since that action is not performed by the person on himself but on another object (the street).
This is the best answer I can come up with given how you have worded your question.
Even in your revised sentence, it's the street that's being crossed because it's the subject of the sentence.
When a person says, 'I am getting dressed,' they are making themselves the subject. It usually implies that they are dressing themselves, but could also be true if they are being assisted, as by a parent or costumer.
To address the other part of the query, there is an existing, though not very common, idiom. A person 'getting crossed' would refer to them being disobeyed, or thwarted in some action by another person who is 'at cross purposes.' You'd most commonly hear/see this sense in a story where someone says "Don't cross me."
As others have noted, dressing is a reflexive action—you do it to yourself, and when you are finished, you are in a different condition which is called dressed.
Others have also noted that "cross" is transitive; when you finish crossing, you are in a different position. This position is called across the street, that is, on the other side of the street from where you started.
So you don't "get crossed", you get [yourself] across the street.
Incidentally, there is a reflexive sense of "cross". It is called crossing oneself. This is a religious practice, also called making the sign of the cross. See, for example, http://www.kencollins.com/instructions/how-01.htm
