I had recently participated in a tournament and I think there is some manual pairing hidden inside which causes my friend to play against me.
You are wrong. To a trained arbiter the pairings are very obviously correct. With 128 players, all but 4 of them unrated (and those 4 ratings are not FIDE ratings, they are likely estimated ratings), nobody in their right mind is going to try pairing by hand and nobody in the organization of such a large event cares anything about two insignificant players out of 128. Running a tournament with 128 players is an enormous amount of work and fiddling with the pairings is only going to make it worse.
Let me explain the 5th round pairings.
Here is the position after 4 rounds. You will see that 7 players are on 4/4 and 2 players are on 3.5/4 and the players on 3.5/4 actually played each other in round 3. Your friend has the lowest starting rank of the 7 with a starting rank of 124. Of the two players on 3.5 you have the highest start rank of 38.
If you check the scoring of each of these players including colour, which you can do by clicking on their name in the list, you will see that 4 of the 7 players on 4/4 have the colour sequence WBWB and so are due white in round 5. Three have the colour sequence BWBW and so should have black in round 4. The 3 players expecting black are paired against the top 3 players expecting white according to start rank number. The odd one out is you friend who is expecting to play white.
So, your friend is down floated to the 3.5 score group. If we look at the colour sequences for the two players there we see that you are expecting black and the other player is expecting white. You and the other player on 3.5 played each other the round before. You cannot be allowed to play again. Your friend is expecting white and you are expecting black so the two of you are paired against each other and the other player is down floated to the 3/4 group. If the colour history for you and the other player on 3.5 were reversed then the other player would have been paired against your friend and you would have been down floated.
The pairings are exactly as would be expected.
If you want to check the pairings yourself then you will need a copy of Swiss Manager, the pairing program that was used. You can order a copy here. You will need the full version costing 150 euros because there are more than 50 players in the tournament. You will also need the help of somebody familiar with the program because it is not very intuitive.
