edge case in character builder won't offer me Eldritch Knight 2nd level spells

I built a Barbarian 1, Cleric 1, Fighter 6, Rogue 6 character.   I just added the 6th level of fighter, expecting to have access to level 2 spells.

The Builder correctly says I now have 2 second level spell slots.  This is from Multiclass Spellcaster: Spell Slots per Spell Level table, using the equation (Cleric level) + (Fighter level / 3) + (Rogue level / 3) = Level 5.  Builder gets this right.

The problem is when I go to Spells -> Manage Spells -> Fighter -> Add Spells.  There I am not offered any 2nd level spells.  RAW says I should be able add a spell for a level I have a spell slot for.  Builder says I have a level 2 slot, but won't let me select a level 2 spell.

The Eldritch Knight Spellcasting table doesn't grant me any more spells at level 6, but the text says "Whenever you gain a level in this class, you can replace one of the wizard spells you know with another spell of your choice from the wizard spell list."  Which implies "at a level you have slots available for."  I Removed a 1st level spell, so Builder reported I had Known Spells: 3/4.  So I had a replacement spell to select, but I was not offered level 2 spells.

I will be glad to be told the error in my logic, or be glad to be offered a fixed Builder.  A temporary workaround would also be useful.

I left "Copy of Logar" in my character list to save time recreating the issue.

Spell slots are determined based on the Multiclassing table. But each class/subclass must prepare spells as if they are a single-classed character and Eldritch Knights don’t learn 2nd level spells until they are 7th level. You will need one additional level of fighter to gain 2nd-level spells as a EK (same for Rogue if an Arcane Trickster), and you will need two additional levels of Cleric to gain 2nd-level Cleric spells.

Stormknight,

Thank you for posting the rules that I explained in my original post.  As I suggested there, either point out which rule I got wrong or fix the character builder to match RAW.

John Light

Since you don't want to read the rules yourself:

Spells Known and Prepared. You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class. If you are a ranger 4/wizard 3, for example, you know three 1st-level ranger spells based on your levels in the ranger class. As 3rd-level wizard, you know three wizard cantrips, and your spellbook contains ten wizard spells, two of which (the two you gained when you reached 3rd level as a wizard) can be 2nd-level spells. If your Intelligence is 16, you can prepare six wizard spells from your spellbook.

Each spell you know and prepare is associated with one of your classes, and you use the spellcasting ability of that class when you cast the spell. Similarly, a spellcasting focus, such as a holy symbol, can be used only for the spells from the class associated with that focus.

As Sposta pointed out in their comment.  Cleric 1 means only 1st level cleric spells, EK 6 means, only 1 level wizard spells, Rougue 6 (AT) means also only 1st level wizards spells.

So, conclusion - nothing wrong with the builder the builder is following RAW