Christian Fish Symbol
Which way does the fish swim?
Which way should the Christian fish symbol face?
The Christian fish symbol or 'Jesus Fish' is conventionally shown swimming from right to left. And there are two likely reasons for this:
Christ overcomes evil with love. He comes from righteousness (symbolised by the right side) to confront evil (symbolised by the left side).
If a 'Jesus Fish' faces the opposite way (left to right) this is not 'wrong' or sacrilegious; it simply symbolises the complementary analogy of Christ carrying us from the left, evil side of life, to righteousness on the right-hand side of God. (Similarly in Western Christianity when signing the cross, the fingers trace a line from the left shoulder to the right shoulder.)
In other words, the direction is related to the right side's connection with righteousness. (See also Why is right, right?)
when text is added to the symbol, for example 'Jesus' or 'ΙΧΘΥΣ', aesthetically it looks better to have the first letter of in the mouth of the fish rather than its tail. (The opposite direction is true for right-to-left writing, such as Arabic or Hebrew.)
But no need to get into deep water about any of this. If you believe the direction of a symbol is in some way important, then there's a good possibility you are just being superstitious. The direction doesn't matter a hoot in comparison to the meaning you understand by the symbol.