That's not bad logic, but it's not correct. When he says "where fire resideth, shadows twist and shrivel" he is talking about "disparity", which was mentioned in dark souls 1 opening. Disparity means "differences", and refers to the fact that things used to be always the same never changing when the dragons were in control; everything was gray and nothing lived or died. But when the fire showed up disparity happened, causing life and death to happen, causing light and dark to appear where it was only gray before. So this first part is basically saying "when there is fire there is also dark/shadow" talking about how the first flame created both light and dark and that there can't be light without there also being dark (this is true actually. Try turning your lights out at night and look for your shadow...you won't see it. Same thing if you go outside at night. In darkness there are NO shadows, because shadows are created by light touching objects.) The final part "but in the abyss there are shadows none" means the same thing, that if you let the fire fade and embrace the abyss then you'll find out that it's not so dark and evil afterall.
The connection to Eygon is that he is afriad of the Abyss taking away Irina from him; meaning he is afraid of the "shadows" that Irina says are always biting at her because if they do get her he would lose her. T