These are banned because the bishop has determined that their lyrical content is contrary to Catholic faith in some regard, either explicitly or implicitly. I will list where I think the biggest issue lies in each, since to my knowledge the bishop has not given explicit explanations for each one. Some people jump immediately to Eucharistic heresy as the explanation, but I don't think that's the case for all of these. It's not a heresy to call the Eucharist bread and wine or wheat or anything like that. Jesus calls Himself the "living bread" in John 6. If the hymn denies the real presence, that would be heresy, but saying that it reduces the Eucharist to mere food just because it calls the Eucharist by the names of bread and wine is a silly thing to think.
A few years ago, the USCCB published a document on liturgical music where they essentially said hymns can't contain heretical lyrics. The bishop of this diocese has just taken some action on that guidance.
All Are Welcome
Let us build a house where prophets speak/And words are strong and true/Where all God's children dare to seek/To dream God's reign anew
"To dream God's reign anew" seems to suggest that the members of this house where all are welcome are meant to recreate God, or at least the activity of God in the world, in their own image, since they "dream [Him] anew." Apparently, the use of "water, wine, and wheat" instead of just wine and wheat in this song also indicates that the Eucharist is just a meal of ordinary elements, since water is not as important as an element of the sacrament as are wine and wheat (made into bread).
Ashes
We rise again from ashes to create ourselves anew.
Of course, we do not create ourselves anew. God does. This is blatant heresy. In the OCP publications, this line was changed to remove blatant heresy a few years ago when the USCCB published the document mentioned above, meaning the publishers must have been fully aware of this issues. I mean, this is the most blatant case I've seen in a Catholic hymnal.
Bread of Life (the Bernadette Farrell one)
We eat this living bread,/we drink this saving cup:/sign of hope in our broken world,/source of lasting love.
Although I still don't think this is necessarily a problem, I imagine that the bishop took issue with the use of the word "sign" here, which may indicate that the Eucharist is a mere symbol of Christ's presence. I don't think it has to mean that, but I don't fault the bishop for being concerned that this word might communicate that idea to the faithful. It would be a reasonable concern, if that were his motivation.
Celtic Alleluia
The Word of the Lord lasts for ever./What is the Word that is living?/It is brought to us/through his Son Jesus Christ.
The living Word is Christ. Saying that it is brought to us through Christ seems to indicate that Christ is not the Word.
Covenant Hymn
This whole hymn makes no sense. You can read the full text here. It has some vague biblical imagery, but doesn't really teach us anything about God. It's unclear who the speaker even is, and I could imagine this being a song a man sings to his wife on their wedding night. It also seems to say things about accepting whatever we do, when God doesn't do that. If we deny Him, He will deny us. That's what Scripture says.
For the Healing of the Nations
All that kills abundant living,/let it from the earth be banned;/pride of status, race, or schooling,/dogmas that obscure your plan./In our common quest for justice/may we hallow life's brief span,/may we hallow life's brief span.
To me, this smacks of religious indifferentism, especially as it seem to denigrate "dogma." It pretends that correct dogma is unimportant. It reminds me of that line in one "translation" of Ubi Caritas that says "No race nor creed can love exclude/if honored be God's name." No idea why the bishop did not also ban this version of Where Charity and Love Prevail, since it contains blatant heresy. Love will exclude any false creed. Dogma matters, and it's a good thing.
God Has Chosen Me
I'm gonna stop you right there. God has chosen you? How do you know? Many are called, but few are chosen.
Haleluya! We Sing Your Praises
This one isn't even associated with a composer. If I found the right one, it has Jesus saying "I am bread I am bread" and "I am wine I am wine." This is not correct. It is fine for Jesus to say something like "I am the Bread of Life." The phrase bread of life refers specifically to the Body of the Lord in the Eucharist. Or "this bread" referring to the bread of the Eucharist is a fine phrase. Jesus would not say "I am bread." He's not. He's the Son of God.
Led by the Spirit
The document from the USCCB critiques this one as follows:
“Led by the Spirit,”10 Verse 4: “Led by the Spirit,
now sing praise to God the Trinity: The Source
of Life, the living Word made flesh to set us
free, The Spirit blowing where it will to make us
friends of God …”: “Source of Life” is applicable
to all Three Persons, and in particular to the
Holy Spirit, who is confessed in Catholic usage
as “Lord and Giver of Life.” This doxology is
therefore most ambiguous. Is the Word God?
What relation does He have to “Source of Life”?
This doxology, in trying to avoid both “Father”
and “Son” language, in effect deconstructs the
Trinity into three names whose status, except
for the first, is ambiguous at best and who seem
unrelated. We are very far from the baptismal
formula here.
Many and Great
Overall, the lyrics seem to create a sense that the bread and wine of the Eucharist are ordinary, when all four verses are taken together. They can be read here. Verses 2 and 3 are about wheat and wine, and verse 4 parallels them with imagery about... pebbles. Not a very great way to speak about the Eucharist.
Table of Plenty
O come and sit at my table/where saints and sinners are friends./I wait to welcome the lost and lonely/to share the cup of my love.
This line seems to indicate that one who has not repented of sin may "come to the feast," as it were. But mortal sin must be confessed before one may partake of the Eucharist.
Three Days
The third verse says that Christ is still pierced and still suffers every day. This is a heresy, and actually one that Protestants often wrongly accuse Catholics of holding. The Mass is a representation of Christ's sacrifice. He is not sacrificed again and again each day. Scripture says that Christ made one sacrifice for all.