Saint Augustine sums this up where it makes absolute sense to me when he says....
“You hear the Lord himself declare: ‘It is not you that speak, but the Spirit of your Father that speaketh in you’. Likewise you hear the Apostle declare: ‘God hath sent the Spirit of His Son into your hearts’. Could there then be two spirits, one the spirit of the Father, the other the spirit of the Son? Certainly not. Just as there is only one Father, just as there is only one Lord or one Son, so there is only one Spirit, Who is, consequently, the Spirit of both. . . Why then should you refuse to believe that He proceeds also from the Son, since He is also the Spirit of the Son? If He did not proceed from Him, Jesus, when He appeared to His disciples after His Resurrection, would not have breathed on them, saying: ‘Receive ye the Holy Ghost’. What, indeed, does this breathing signify, but that the Spirit proceeds also from Him?” (De Trin. II, 5, 7-10; IV, 18, 24 )
The Holy Spirit, as regards His existence, proceeds only from the Father. That is the most fundamental revealed truth about the Spirit and the dogma of the Church of the Seven Councils. There is only one cause of the Spirit, the Father, who is the cause of everything and all, just as the Father is the cause of the Son.
As far as I know the Latin Church does not teach double origin. The Father is the source of both the Son and the Spirit.
The Greek word used for proceed is ekpouremai, which, unlike the Latin translation, implies origin.
The Catholic-Orthodox dialogue, some years back, pretty much settled this issue by acknowledging the above. The Orthodox agree that the Spirit is sent by the Father as well as the Son, that Both share the same Spirit (this is made perfectly clear in the Palamite doctrines that pretty much represent official Orthodox teaching), but it is of utmost importance to realize that the Father is the source of the Spirit as far as His existence is concerned, and that the Son is not the source; double origin or double source is not the doctrine of the Church, never was and never will be. It is extremely important to distinguish the source of existence of the Spirit as being only the Father, thus preserving the monarchy of the Father.