Trinitarians say that the Spirit of God is not God the Father but another separate person. This statement is illogical. Why this is so becomes clear when one understand what the "spirit" is. The Hebrew word for spirit is Ruach, Ruach means "mind", so when a Trinitarian says that the Spirit of God is not the Father but another person, it is like saying: "The mind of God is not God himself but someone else." This statement is illogical, the mind of a person cannot be someone else.
God is only one person, and the Spirit of God is God's "brain," God's spirit ist everything what god is, he is Power and Wisdom.
It is written that God made man in his own image, when he breathed his spirit into Adam's nose, he gave him a part of his "mind," Adam's character was like God's character. And when man dies, this breath goes back to God.
God the father = The Spirit
The Spirit has begotten = The Son
The Son = the same Mind
And when he had said this, he BREATHED into them and spoke to them: Receive the Holy Spirit!
Since you did not present Scripture I will using the Teachings of Jesus who distinguishes the Father from the Holy Spirit and the Son from the Holy Spirit. They are not each other but distinct in Person as seen by the use of personal pronouns by Jesus below.
John 14-16 Jesus teaches the Holy Spirit is distinct from the Father and Son
John 14:16-17
16 "I will ask the Father, and He will give you
another Helper, that He may be with you forever;
17that is the Spirit of truth, whom the world cannot receive, because it does not see Him or know Him,
but you know Him because He abides with you and will be in you.
John 14:23
My Father will love him, and
We will come to him and make
Our abode with him.
John 14:26
26 "But
the Helper, the Holy Spirit, whom
the Father will send in My name,
He will teach you all things, and bring to your remembrance all that
I said to you.
John 15:26-27
26 "When
the Helper comes,
whom I will send to you from
the Father,
that is the Spirit of truth who proceeds from the Father,
He will testify about Me,
27and you
will testify also, because you have been with Me from the beginning.
John 16:5-8
"But nowI am going to Him who sent Me; and none of you asks Me, Where are You going?'
6"But because I have said these things to you, sorrow has filled your heart.
7"But I tell you the truth, it is to your advantage that I go away; for if I do not go away,
the Helper will not come to you; but if I go,
I will send Him to you.
8"
And He, when
He comes, will
convict the world concerning
sin and
righteousness and
judgment;
John 16:13-15
13 "But when
He, the Spirit of truth, comes,
He will guide you into all the truth; for
He will not speak on His own initiative, but whatever
He hears
, He will speak; and
He will disclose to you what is to come.
14"
He will glorify Me, for
He will take of
Mine and will disclose
it to you.
15"All things that
the Father has are
Mine; therefore I said that
He takes of
Mine and will disclose
it to you.
Matt 28:19-20
Go therefore and make disciples of all the nations, baptizing them
in the name(singular not plural names) of
the Father and
the Son and
the Holy Spirit
hope this helps !!!