While I agree with you that this is absolutely the way the spell is intended to work, the problem that rules lawyers have can be laid out below.This is not technically true. See the description of
Area in the SRD. This is mirrored in the RC as Arrowhawk points out above. The key phrase is "you select the point where the spell originates." And it is clear from an objective reading that this point, generally referred to as the "point of origin" or PoO, can be anywhere within the range of the spell. Thus, the argument goes, a caster who is completely inside an antimagic field ought to technically be able to cast a fireball spell so long as the caster places the PoO outside of the antimagic field. Obviously, this is patently ridiculous. As Greenfield states above, such an interpretation would make the spell broken. Period. But I digress. What part of the caster? What happens when the caster is in the AMF, but his hands (or other body parts applicable) are not and he casts a somatic spell? One could argue a Small or Medium creature standing on the edge of an AMF could cast under such circumstances, since they have 5 foot reach after all.
No, this is not really arguable. A creature occupies the space that they occupy and can only extend out within their reach for the purposes of making attacks. That is the only situation for which the rules ever allows a creature to theoretically be somewhere other than the square(s) it occupies. It might make some logical sense that a caster ought to be able to poke his head outside the area of effect to speak the verbal components and stick his fingers out to use the somatic components, and if you are such a DM, this is all well and good. But the game rules don't allow for it. If they did, it would open up a huge can of worms for all area effects in general. Suppose a caster stuck on the edge of a web spell wants to argue "but my hands were outside the area when the spell was cast so they are free to cast spells right?" This kind of argument ad nauseum.As I pointed out, the definition of the point of origin is actually pretty specific. It has to be at the intersection of a gridline and within the range of the spell, but the caster chooses it. If it weren't for this, the argument over antimagic field probably wouldn't exist to the extent that it is, but this is so, and thus the argument is there.
But for myself, I can't see any designer ever thinking that a wizard could sit inside an antimagic field and cast horrid wilting, fireball, or whatever on targets who are outside it and believe that to be balanced. Most people agree. Rules lawyers don't because the spell is worded poorly. I prefer to interpret the rules in the spirit of balance and say that all magic has to originate from the caster before any point of origin is determined. So the sitting safely inside the AMF and casting out of it is not possible.
I can entertain the argument that a caster inside an AMF could cast mage armor on himself then step outside and have the spell become active, but in my opinion, that still crosses the line. Consider the wizard who casts AMF then proceeds to cast every single buff spell in the world before dismissing the AMF. If he is standing somewhere (say on a high ledge) where he is practically unreachable, then he is nigh invulnerable until he decides to switch off the AMF, at which point, because of his buff spells, he IS invulnerable for all practical purposes. Compare that to time stop, which only gives you 1d4+1 rounds to buff. And time stop is a 9th level spell. Obviously a 6th-level spell can't be so much better. Sometimes you just have to use the greater context of the game to guide your interpretation of the rules.
Therefore I consider the term "suppress" to be a little more broad than some rules lawyers might argue. Magic just doesn't work inside an AMF. And the only magic effects that persist, are those that existed before the AMF was cast. So 1) cast mage armor, 2) cast AMF and the mage armor is active but suppressed. Do it the other way around where 1) cast AMF, 2) cast mage armor, and the mage armor spell fails. It isn't practical to interpret the spell any other way IMHO. I acknowledge that the technical case for an argument is there, but it wouldn't make sense in the greater context of the game.