Is there a way to indicate that somebody is your girlfriend without using the possessive term my? I think saying She/He is my partner/other half is OK for married people, but it doesn't feel right for girlfriends and boyfriends.
You could keep the possessive but drop the objectifying label of girlfriend (but only if you're ready to get serious, yknow?)
She's is my everything. She is my reason for waking up in the morning. She is the best thing that ever happened to me.
In the above, you've replaced "girlfriend/sweetie/main squeeze", which as nouns suggest ownership, with descriptive phrases where you are owning your feelings instead.
Personally, I'd go with just "my girlfriend." Sometimes it's nice to feel like someone is all yours.
You can't really say She is [some word] girlfriend/partner/whatever without using "my". As others have said, "my" in such usages doesn't significantly imply "possession", so there's no reason to avoid it on those grounds. But OP doesn't like it, so let's press on...
If you used "a", it would imply she's just one of several girlfriends/partners.
People do sometimes say things like "Meet the girlfriend", but it's not standard English.
I suggest OP forgets about constructions starting with "She is...", and considers getting the information acrosss in a different way - by saying, for example, "We go out together", "We are an item", "We live together", or whatever variant is closest to the truth.
You are incorrectly parsing this sentence:
She is my girlfriend
You are showing confusion as to what term the adjective "my" is modifying. It is modifying "girlfriend", not "she". You do not own her, you own your relationship to her.
It is very different from this phrase:
She is my girl.
Here "my" is most certainly modifying "girl" and asserting ownership over the person and not the relationship.
If your relationship to her is clearly defined by the term "girlfriend" then you will be most clear by saying that "she" is the person to whom "you" feel this relationship.
As an illustration, let's replace "girlfriend" with a different relationship term, "hero". If you say:
She's my hero.
You are not implying anything of ownership, or for that matter even reciprocity in your relationship to her. This is because "my hero" is the descriptive phrase, not "she's my".
All you are claiming ownership of with "She's my girlfriend" is your relationship to her. Not to her person.
Lots of good stuff. As to the general "my", I give you an excerpt from C.S. Lewis' "Screwtape Letters", behind this finely-crafted link.
"My" has lots of different meanings. Ownership is just one of them.
Boyfriend/girlfriend doesn't automatically mean exclusivity, or ownership. Gay people or polyamorous people sometimes have to introduce their relationships to others with an explicit definition of what the relationship actually is in the introduction itself: "This is Liz, the woman I sleep with". (As opposed to "Liz, my partner" <-- what business are you in?)
So the following get used:
- Liz, the woman I sleep with
- Liz, the woman I'm in a relationship with
- Liz, the love of my life
- Liz, my better half
- Liz, the woman I'm dating
and so on.
Technically while some classify 'my' as a pronoun others classify it as an adjective albeit a personal one showing possession.
"Nomenclature While some classify the words my, your, etc. as possessive adjectives, others, due to the differences noted above, do not consider them adjectives – at least, not in English – and prefer possessive determiners. In some other languages the equivalent parts of speech behave more like true adjectives, however.
The words my, your, etc. are sometimes classified, along with mine, yours etc., as possessive pronouns or genitive pronouns, since they are the possessive (or genitive) forms of the ordinary personal pronouns I, you etc. However, unlike most other pronouns, they do not behave grammatically as stand-alone nouns, but instead qualify another noun – as in my book (contrasted with that's mine, for example, where mine substitutes for a complete noun phrase such as my book). For this reason, other authors restrict the term "possessive pronoun" to the group of words mine, yours etc. that substitute directly for a noun or noun phrase.
Some authors who classify both sets of words as "possessive pronouns" or "genitive pronouns" apply the terms dependent/independent or weak/strong to refer, respectively, to my, your, etc. and mine, yours, etc. For example, under this scheme, my is termed a dependent possessive pronoun and mine an independent possessive pronoun.
 "Possessive adjectives" in EnglishThe "possessive adjectives" in modern English are my, your, his, her, its, our, their and whose (in Whose coat is this?, for example). All of them indicate definiteness, like the definite article the. Archaic forms are thy and mine (for my, used before a vowel, as in It is mine own work).
The possessive suffix -'s works similarly (as in Mary's husband, anyone's guess), but it is a clitic attached to the preceding determiner phrase.
In English, "possessive adjectives" come before any (genuine) adjectives, for example your big blue eyes, not big blue your eyes.
"Possessive adjectives" in English are sometimes misspelled with apostrophes ("it's", "her's")."
Quoted from wikipedia.
Spoken english sometimes differs from written English and colloqually, it really doesnt matter because thats the flexibility spoken language offers, otherwise we will all be uptight
You could say something colloqually
We are dating.
We are going out.
We are partners.
We are seeing each other.
She is going out with me //some ownership
I am going out with her
But really other than understanding the language does it really matters?
I am sorry, but IMHO - the whole concept of this relationship is about ownership. Like a marriage is often seen as an "ownership contract", so does the boyfriend-girlfriend relationship. it can not be avoided by language tricks. it is embedded in the concept of the word relationship itself, no matter how you say it.