Now where then do they take the filioque from? Does anybody have a brief answer?
It's an early example of Latin theological creativity gone awry, a "creativity" that eventually came to be justified in the 19th century under the guise of "development of doctrine."
While "filioque-ism" probably had an innocent origin in the west (due to the western tendency not to carefully distinguish between the "economic" and "eternal" procession of the Holy Spirit), things went bad when it began to be asserted by some that the Holy Spirit "eternally" proceeded from God the Son. The origin of this was two fold...
1) A misguided attempt to bolster the "divinity of the Son" against the remnants of Arianism in some parts of the west (particularly amongst the Germanic tribes) - the belief that saying the Son also
had the procession of the Holy Spirit like God the Father
somehow made the Son seem "more Divine" and hence working against the Arian assertion that the Son was ultimatly a creature, a sort of supreme archangel.
2) Theological speculation as to how the "Spiration" of the Holy Spirit differed from the "Begotteness" of the Son. Some in the west began studying the Holy Trinity as an abstraction, by examining God's unity from the sole p.o.v. of God as one substance, in which the differentation of "persons" solely existed because of the "relations" beween those Persons (i.e. the relationship of the Son being "begotten" from the Father, the relation of the Holy Spirit "proceeding" from the Father, etc.) From this perspective, men with the curiosity of a philosopher, concluded that there was seemingly no differentiating relationship between the "Son" and the "Holy Spirit", hence because of the Divine Unity they are in fact "one Person"...but since that didn't square with Revelation, they concluded that the Holy Spirit had to also proceed from the Son, as He does from the Father. This creates a relationship between the two of them, hence making them two different Persons.
The Holy Scriptures (and the Eastern tradition) never viewed the Holy Trinity in such abstract terms. While it is definately true that the Three Persons are of the same "essence" and this accounts for the Divine unity, the Divine unity is also reckoned as being so because the Holy Trinity has one "source" - God the Father. In the New Testament, whenever you read "God", more often than not it is speaking of "God the Father" - where as the Son and the Holy Spirit are Divine, because they receive and come forth in eternity from God the Father. When looked at this way (and not as an abstraction, which is not how we meet God to begin with - that's putting the cart before the horse), the supposed "logical need" for the filioque clause evaporates...and certainly it has no justification whatsoever from what God has revealed Himself.
Filioque-ism, simply put, is the product of human "logic". It did not originate in the revelation of God Himself - and for human genius to pretend to be able to add to our knowledge of the hidden things of God, is madness.