Short Answer
'his spellbook' should be changed to something more sensible, like "any of their spellbooks" or "any spellbook on their person". The rules expect, for absolutely no good reason, that each wizard has exactly one spellbook and they carry it on their person at all times except for rare occasions when they are securing it hidden away in some variety of magically protected vault. Magically protected vault think and on person think don't seem to be aware of each other and on person think definitely dominates.
It's an easy fix, though-- you can even fix it just by getting creative with your definition of 'his spellbook' and claim that the RAW kinda works1
RAW Silliness
'his spellbook' is used several other times in the text. Let's look at what it means:
A wizard may know any number of spells. He must choose and prepare his spells ahead of time by getting 8 hours of sleep and spending 1 hour studying his spellbook. While studying, the wizard decides which spells to prepare.
A wizard begins play with a spellbook containing...
(emphasis added)
At each new wizard level, he gains two new spells of any spell level or levels that he can cast (based on his new wizard level) for his spellbook. At any time, a wizard can also add spells found in other wizards’ spellbooks to his own (see Magic).
Spells Gained at a New Level: Wizards perform a certain amount of spell research between adventures. Each time a character attains a new wizard level, he gains two spells of his choice to add to his spellbook. The two free spells must be of spell levels he can cast.
A wizard must study his spellbook each day to prepare his spells. He cannot prepare any spell not recorded in his spellbook, except for read magic, which all wizards can prepare from memory.
Wizards perform a certain amount of spell research between adventures. Each time a character attains a new wizard level, he gains two spells of his choice to add to his spellbook.
Wizards can add new spells to their spellbooks through several methods.
A wizard can also add a spell to his book whenever he encounters one on a magic scroll or in another wizard’s spellbook.
If the bearer is a caster who prepares arcane spells, he may prepare this spell as if it were in his spellbook.
(Wayfinders)
However, this would allow a wizard to copy a spell into his spellbook so he could prepare the spell from his book (assuming the spell takes up only one page...
(Memorize Page)
So, whatever 'his spellbook' is, it's the same 'his spellbook' that the Wizard has to study to prepare spells and that spells are instantly poofed into when the wizard levels up.
The spellbook a wizard starts with may or may not be 'his spellbook'; the rules refer to it only as a spellbook, much like those that can be purchased from the equipment section of the rulebook. Nonetheless, an entity need not be physically present to be studied, and adding spells to 'his spellbook' is possible both through levelling up and through the spell Memorize Page.
Since a wizard's spell are all in 'his spellbook' and a wizard preps by studying 'his spellbook' and adds spells to 'his spellbook' all without ever needing to physically interact with 'his spellbook' all you're doing by exploring the RAW wonkiness here is buffing wizards by making 'his spellbook' harder to destroy/endager/take away. That's... not really helpful for anything ever. Unless you're a wizard trying to protect 'his spellbook', which is currently a bunch of flamable paper in a backpack, in which case convincing your DM that 'his spellbook' is actually merely the platonic idea of a spellbook with no special relation to that specific physical copy may in fact be useful.
In any case, the RAW never specify what 'his spellbook' means, specifically, nor do they specify what ownership, possession, or 'his' means. Spellbook is relatively clear. Since the rules do not define these terms they are free to be defined however the GM sees fit, provided those definitions are compatible with the RAW.
1 Specifically, define a spellbook broadly-- a wizard's spellbook is the thing they stores their spells in. If they store their spells in several books it is the collection rather than any individual book that is 'his spellbook'; the books merely serve as component parts. You can additionally specify that ownership is possession, and more specifically physical possession, so that books in the wizard's personal library back at their estate don't count as 'his'. While this works (the second order consequences for magic items that rely on ownership and such are very much in line with the theme imposed on the wizard by this limitation), it's definitely gymnastic and it's probably simpler just to replace the rule with an equivalent and more clear-on-its-face houserule.
Oh, and obviously the 'his' in his spellbook is gender neutral.
I can see two reasons why the wizard would not be allowed to change her arcane bond.
Mechanical aspect
The main difference I can see between the fighter / sorcerer example and the wizard is that a familiar provides a constant, specific bonus.
One of the risks would then be that the wizard changes familiar depending on the current focus of the campaign. For example, he would start with an armadillo to protect against attacks, then face more spellcasters and replace it with a dodo for the initiative bonus, later change to a pig because the campaign has more social encounters, and so on.
I always assume that the reason fighters and sorcerers can change their class features is because some feats and spells don't scale well. Wizard bonuses don't scale at all, so this concern doesn't exist.
Flavor aspect
Another difference is in terms of flavor: the wizard is bonded to that item or familiar. Another class that has a bonded companion is the paladin, and while a paladin can change her bonded mount, it takes 30 days during which she has maluses to all her attacks.
On the other hand, there is no connection between a fighter and its feats or a sorcerer and its spells.
Would the game break if the wizard was allowed to change its arcane bond, then?
Probably not. That's, after all, the reason it is included in the retraining rules.
However, other players could get jealous that the wizard gets a flexible bonus that can be changed over time. A ranger might wonder why he can't change his favored enemy, a cavalier might want to change his order, and so on. Those are also bonuses whose utility can change over the course of a campaign.
As for the flavor aspect, it depends on the GM and player. Is a familiar a companion of research and travel, who spends a lot of time with and trusts the wizard, or is it a class feature that provides useful constant bonuses? In the former case, you shouldn't allow the players to throw it away, otherwise they might be torn between the mechanical and the flavor choice.
"I'm sorry, Arthur. We spent a lot of time together and I loved you, but now I really need this +3 bonus to swim more than anything. So, goodbye, old friend."
Best Answer
A rather large reason is this:
Basically, if you know you want an awesome ring, but don't want to take forge ring as one of your feats, take a ring as a bonded object and you can add cheap-ish magical enhancements to it when you reach appropriate levels. Whereas taking a wand essentially gives you the craft wands feat, and when the charges are expended allow you to choose a new spell for the wand.
A bonded weapon also has another benefit, granting you a masterwork weapon at level 1 with no cost to you, giving you slightly more benefit at lower levels where you have fewer spells per day (masterwork light crossbow, you're pretty cool).
Staves are very similar to wands in that they give you the benefit of a feat you'd use very little without needing to spend a feat slot on it, though it definitely doesn't come into play until higher levels.
In short, it's the free crafting feats to use on your bonded object that should be the main determining factor in what your object is (unless crafting is disallowed in your game).