Freesurfer question: I ran the same pipeline using two input PET images — one that was left-right mirrored and one that was not

I ran the same pipeline using two input PET images — one that was left-right mirrored and one that was not.
I expected the results to simply be flipped along the left-right axis.
However, the uptake patterns themselves were different, not just mirrored.

How should I interpret this difference?
Why does flipping the input image affect the actual PET signal distribution, not just its orientation?
I need to explain this to my professor — what would be the best way to describe this phenomenon?

i attach the code below.

SUBJECT_ID=“VCI_221”
DATAPATH=“/home/nri/Desktop/{SUBJECT_ID}" OUTPATH="{DATAPATH}”
mkdir -p “$OUTPATH”

T1_FILE=“{DATAPATH}/t1mpr.nii.gz" PET_FILE="{DATAPATH}/wPET.nii”

MNI_TEMPLATE=“/usr/local/fsl/data/standard/MNI152_T1_2mm.nii.gz”

echo “Step 1: T1 → MNI152 (affine registration)”
flirt
-in “$T1_FILE”
-ref “$MNI_TEMPLATE”
-omat “$OUTPATH/t1_to_mni_affine.mat”
-out “$OUTPATH/t1mpr_in_mni.nii.gz”
-dof 12

echo “Step 2: T1 → MNI152 (nonlinear registration)”
fnirt
–in=“$T1_FILE”
–aff=“$OUTPATH/t1_to_mni_affine.mat”
–cout=“$OUTPATH/t1_to_mni_warp”
–config=/usr/local/fsl/etc/flirtsch/T1_2_MNI152_2mm.cnf

echo “Step 3: PET → T1 (rigid coregistration)”
flirt
-in “$PET_FILE”
-ref “$T1_FILE”
-omat “$OUTPATH/pet_to_t1_affine.mat”
-out “$OUTPATH/pet_in_t1.nii.gz”
-dof 6

echo “Step 4: Apply warp to PET → MNI”
applywarp
–ref=“$MNI_TEMPLATE”
–in=“$OUTPATH/pet_in_t1.nii.gz”
–warp=“$OUTPATH/t1_to_mni_warp”
–out=“$OUTPATH/pet_in_mni.nii.gz”

echo “PET → $OUTPATH/pet_in_mni.nii.gz”

echo “Step 5: mri_vol2surf "
for hemi in lh rh; do
mri_vol2surf
–mov “$OUTPATH/pet_in_mni.nii.gz”
–regheader fsaverage
–hemi $hemi
–o “OUTPATH/PET_SUVR_{hemi}.fsaverage.mgh”
–projfrac-avg 0 1 0.1
done”