Owl uses the Help action, rogue uses the Attack action
The owl familiar can approach to within 5 feet of the enemy, use the Help action, then fly away. As was discussed in this previous question, a character doesn't need to stay next to the enemy after using the Help action for their ally to get advantage on an attack. An owl's Flyby ability means it won't be vulnerable to opportunity attacks while doing the last step of flying away (which is why you might prefer that form of familiar over something else). For a rogue, attacking with advantage also enables Sneak Attack (assuming there's no reason they'd also have disadvantage), even if there's no other ally nearby.
Held actions are only needed in defense against the combo
The combo is not foolproof though. Clever enemies will see what is happening and adapt. For instance, if they have ranged weapons, they might prioritize bringing down the owl by sending an attack or two its way, even if they have disadvantage on their attacks from the rogue being up in their face. And melee-exclusive monsters can hold their action to attack the familiar when it swoops down to be near them. Familiars have very few HP and low armor classes, so a single attack is often enough to do them in.
The combo is good, but probably not overpowered
Spending an hour resummoning the familiar after a fight is often impractical in the middle of a dungeon (even if you have the material components available), so the rogue can't exclusively rely upon using their familiar for their sneak attacks, even if it is very good when it works. A crafty DM might want to get rid of the rogue's familiar in an earlier fight (even at the cost of doing less damage to the rogue) if they don't want the combo to make the fight against the final boss of the dungeon too easy!
Different monsters' reactions can help with world building
A particularly skilled DM might use different reactions by different kinds of monsters to clever combos like this one to teach the players about the monsters, and about how they fit into the wider game world. If you try this trick on an ogre, it may keep on working indefinitely because ogres are pretty stupid and often get tricked into things by other creatures (such as the BBEG). If you try it against a gang of scheming goblins, one might catch on quickly and call out a warning to the rest (do any of the PCs speak goblin?), because goblins are reasonably intelligent and work well in groups. If you try it against a wizened ancient dragon, they may see your tricks coming a mile away and react appropriately even before you've used it against them even a single time (as a long-lived creature with truesight, that dragon has seen much more powerful tricky maneuvers fail many times before, and it's not at all hard to obliterate a familiar with a big AOE breath weapon that also gets most of the rest of the party).