BSF
Explorer
By the rules, you are correct. However, house rules trump the rules as written. 
OK, so you want to argue against the house rule.
By this wording, you really cannot counterspell at all since interrupting with a readied action is the condition which makes counterspell work. To house rule this, you need to make a bunch of conditional statements on how readied actions work for spells. Without the conditionals, it breaks down to you cannot interrupt a spell with another spell. With conditionals, you can only interrupt a spell with a dispel magic used as a counterspell, or with a readied action to use the same spell to counterspell, or you cannot use a spell to interrupt another spell. The language starts to get a bit silly.
In the end, it really isn't that big a deal to have damage dealing spells interrupting spells and forcing a concentration check. A fighter standing in front of the spellcaster can still interrupt with a sword. An archer could ready an attack with his bow. The invisible rogue could still throw a dagger from 25' away for a sneak attack to interrupt the spell. Your DM needs to design opponents that take these tactics into consideration, is it really necessary to prevent other spellcasters, that have readied a damage dealing spell in the event that the enemy casts a spell, from doing the same?
Remember that using a readied action isn't "I will ready a counterspell, or a dispel, or a magic missile in case the BBEG casts a spell." It is "I ready a counterspell if the BBEG casts a spell." Or, "I ready a magic missile if the BBEG casts a spell." This doesn't preclude the BBEG seeking cover, drinking a potion, using a wand, etc. Readied actions are useful only as responsive tactics to a predicted course of action.
To me, it sounds like you have caught the DM a little off-guard and his initial reaction might need to be rethought. Changing tactics around, and using the PC's tactics against them once in a while goes a long way toward reducing the concerns of a magic missile interruption on a spell. It is still a good tactic, when it works, but it is not that overpowering.

OK, so you want to argue against the house rule.
In this case, he is the DM of this group, and he wants to house rule it that you cannot interupt a spell with another spell with the same casting time by use of the ready action.
By this wording, you really cannot counterspell at all since interrupting with a readied action is the condition which makes counterspell work. To house rule this, you need to make a bunch of conditional statements on how readied actions work for spells. Without the conditionals, it breaks down to you cannot interrupt a spell with another spell. With conditionals, you can only interrupt a spell with a dispel magic used as a counterspell, or with a readied action to use the same spell to counterspell, or you cannot use a spell to interrupt another spell. The language starts to get a bit silly.
In the end, it really isn't that big a deal to have damage dealing spells interrupting spells and forcing a concentration check. A fighter standing in front of the spellcaster can still interrupt with a sword. An archer could ready an attack with his bow. The invisible rogue could still throw a dagger from 25' away for a sneak attack to interrupt the spell. Your DM needs to design opponents that take these tactics into consideration, is it really necessary to prevent other spellcasters, that have readied a damage dealing spell in the event that the enemy casts a spell, from doing the same?
Remember that using a readied action isn't "I will ready a counterspell, or a dispel, or a magic missile in case the BBEG casts a spell." It is "I ready a counterspell if the BBEG casts a spell." Or, "I ready a magic missile if the BBEG casts a spell." This doesn't preclude the BBEG seeking cover, drinking a potion, using a wand, etc. Readied actions are useful only as responsive tactics to a predicted course of action.
To me, it sounds like you have caught the DM a little off-guard and his initial reaction might need to be rethought. Changing tactics around, and using the PC's tactics against them once in a while goes a long way toward reducing the concerns of a magic missile interruption on a spell. It is still a good tactic, when it works, but it is not that overpowering.