Agreed.
When the word "invasion" is used in the context of people entering a country, it's to say these people are invading and taking over on behalf of another country. If these people are seen as soldiers of a foreign enemy, then it's ok to shoot them.
It doesn't have to be "on behalf of another country", nor does someone have to be a "soldier" nor "seen as an enemy" in order to invade. Any unwelcome intrusion into another's domain is an invasion. Whenever someone comes into our country unwelcomed, they are invading our country. Same as whenever someone comes into your house unwelcomed. They are invading your house.
And no, the country isn't a macro version of the home. Everything from the rules to ownership is completely different.
Is that so?? You are a citizen of your house, just like you are a citizen of your country. The population of your country is ~330 million (that's not including adjustments for the illegals who are currently invading it). The population of your house is yourself, any spouse/children you might have, and any other friends/relatives you might have "granted citizenship" to reside inside it. The idea of citizenship, whether inside of a particular house, or inside of the USA, is all the same. You don't want people unwelcomely intruding into your house, your school, your church, your city/township, your state... so why would you be okay with people unwelcomely intruding into your country? It's the same concept, just on a different scale.
I think many of us, as individuals, have largely forgotten the importance of community, whether that be within the family, within the city/township, within the church, within the school, ... ... ...
I think many of us have also largely forgotten the importance of being able to properly govern oneself. Without being able to properly govern ourselves as individuals, how can we expect to properly govern in a more "macro" way, such as over various communities and localities, let alone over a state or a country?
And asking for asylum isn't illegal.
Not everyone is "seeking asylum"...