It is important to understand what is presented on the page
What is the mind? first.   Please, read that page first.

Because the mind/ego/false self thinks it is separate and needs
to fight for its survival, which is supported by the unloving part
of this world, plus it cannot tell truth from falseness, it creates
its own world according to its own ideas, assumptions, rationalizations,
and judgments.   Because all of that is based upon falseness
it cannot lead to good spiritual health, to enlightenment, to true love,
to congruence (harmony) with Divine Loves (Gods).
Thus, individuals who intend to evolve spiritually need to transcend
the mind/ego/false self.

The intent of this article is to bring to conscious awareness one of
the ways the mind creates its own false world, which may trap
an individual and obstruct his/her spiritual evolvement.
It pertains to mental and emotional attachments to things and
people = to possessiveness.
This possessiveness is reinforced and cultivated by the limitations
of language.   Within the scope of this article it is the use of
possessives: my, mine, your, yours, his, her, hers, our, ours, their,
theirs, to have, to own.
They suggest that something or someone belongs to you (or someone
else), while in truth nothing belongs to you or anyone else, not a physical
thing, nor a person, nor a formless thing like power, mind, thought,
consciousness, God, etc.   Things and people come into the life you
live as tools to help you, and while they can stay with you for even
a long period of time, you don't truly own them.

You are an individual manifestation of Awareness ("I Am" = I Awareness
manifested).   Also, you are an individual manifestation of Love (or Light).
Both statements are correct within their respective contexts, though the
first statement is a deeper truth (Love is a pretended manifestation of
Awareness).   Using the popular analogy of an ocean and waves, a wave
is an individual manifestation of the ocean, but it is not separate from
the ocean - it is part of it.   If such a wave would claim that it owns
the seagull that's resting on it, or the fish that's swimming in it, or
the driftwood it carries, or that the power the wave carries when it hits
the shore belongs to the wave, it would sound ridiculous and foolish.
So it is with you.   You, as the individual manifestation of the ocean of
Love you are, cannot claim ownership of anything or anyone and remain
congruent (in harmony) with "your" higher Selves and Divine Loves (Gods).
Not being congruent (in harmony) = being stuck spiritually.

You can pretend-claim ownership of things and people (my son, my husband,
my car, my thoughts, my spiritual power, etc.), but then you get entangled
in your ego, in your false self, and you forsake the ocean of Love you come
from.

It is OK to use possessives, as long as you are aware of
their limitations (as mentioned above) and use them so
others can understand what you're saying, what you mean.
Even better is to find different, more congruent wordings
when possible.
Some examples:
my car --> the car I use
my Godly Self --> the Godly Self of whom I am
my wife --> referring to her by her first name, or
                    the girl/woman I live with/I share life with
my husband --> referring to him by his first name, or
                        the man/guy I live with/I share life with
my son/daughter --> referring to him/her by his/her first
                                name, or the child I share life with
my psychic ability --> the psychic ability that I manifest/channel
my mind --> the mind, or this mind
my body --> the body, this body, the body I use
my life --> the life I live

These more congruent wordings might seem more elaborate,
but their benefit is that you actively demonstrate your awareness
of the spiritual truth.   Also, this helps you to deprogram your
consciousness of this false concept of possessiveness.

David R. Hawkins writes in the highly-energized book
"I, Reality and Subjectivity" about a temptation that has been
encountered by those that attained to higher levels of consciousness,
a temptation to entrap the individuals and bring them down
spiritually.   On page 259 David R. Hawkins writes:
The luciferic temptation that occurs at this level is subtle
and sophisticated.   It plays on advanced but as yet incomplete
spiritual knowledge and understanding.   The presentation is
as follows:   "Now that you are released from the attachment of
love and realize that all karma was only based on illusion and that
there is no fearsome, judgmental God or any 'others' to be
encountered, and now that you are beyond form and therefore
beyond karma and totally free, your power is unlimited.   Own that
power as yours."   The offer is to join the power for power's sake
and reign in the luciferic domain.   The temptation is to
the spiritual ego to obtain God's power but to reject God's love.
When this (temptation) was refused, it retreated.

Again, it's worth repeating:
All owning, having, and possessing is only pretended from the
viewpoint of the spirit = of who you really are.
It is congruent to have, to own things and use them, as long as
you don't become attached to them mentally and emotionally.
The ego, however, likes to become attached to things and
people and declare them as "mine" (my wife, my car, my power, etc.)
It is this mental and emotional attachment of the ego that creates a barrier
to spiritual evolvement and to true love.