Why are some hotels asking you to book through Booking.com instead of matching the price at the front desk?

Simple answer – they already sold the rooms for the low price to booking.com. Why should they lower their prices when they can sell further rooms for a even higher price?
It’s still possible that the rooms given to the customers of the portal have or don’t have certain features regular rooms may or may not have.

In Europe/Germany there investigations ongoing related to booking.com’s and expedia (and friends) pricing practice.

Essentially they compel hotels not to offer their rooms cheaper anywhere else. To enforce this they have reduced the rank of hotels they felt undercut them. This is anti-competitive and is being investigated. However, the sites also have a right to make people not only use them to look and then book elsewhere, this can include the price matching you mentioned.
Eu complaint by Nustay

2: UPDATE: THere have been a few rulings, Booking.com lost:
wsj article about Germany, France italy (paywalled) , Czech ruling , Russian ruling

As someone who runs an events business that regularly organises to resell bulk quantities of rooms with hotels, I can offer one reason colloquially from experience that builds off other answers:

While other people have identified that reception staff may not have the capacity to actually change the price to match booking.com, they may want you to use the website so that the room is booked under the block of rooms available to booking.com at that price. Yes, you can argue this technically goes under the umbrella of “accounting/bookkeeping reasons” but it’s very likely that there is an agreement between the hotel and booking.com that X number of Y type of rooms will be able to be sold at Z rate (discounted) for a certain date range – they probably don’t want to sell all the rooms in the hotel at that (probably) low rate. The reason the booking.com deal exists in the first place is for various advertising reasons brought up in other answers.

In practice, it’s likely that there will be a cap on the number of rooms for a certain date range booking.com can sell at that price. If the front desk matched the rate, that wouldn’t necessarily decrease the number of rooms at reduced price available to booking.com, resulting in an overall reduction in revenue for the hotel in a scenario where the marginal room-night was going to be sold anyway.

So for example in a figurative tiny hotel with 15 rooms available on 1 night (scale up to real life in your head as necessary), where booking.com had the rights to sell 5 of those rooms at USD50 per night, whereas the normal price was USD100 per night – in the scenario where the front desk matches the price, and all rooms are sold, the hotel loses USD50 in revenue (because after selling you a USD50 room, they still have to let booking.com sell 5 USD50 rooms). Whereas if they tell you to use booking.com, your USD50 room is one of the 5 sold through booking.com and if enough rooms are sold, the hotel does not miss out on revenue.

The potential follow up of “but why can’t the front desk just count it against booking.com’s block” is some combination of communicating with people is hard/time expensive, the contract may or may not allow it, and again non (upper?) management staff may not have the capacity.

According to an acquaintance of mine that runs a hotel, sites like booking.com have rules that require the complete transaction to be completed through them. They don’t want the hotel owner contacting you directly and arranging payment in a way that cuts out the website. Not only does the website not get their commission, but the customer doesn’t have the protections that they’d have if they went through the site. You see scams like this more often on Airbnb than on hotels, but it’s still a possibility. The site’s terms of service protect both the site and the customer by preventing them from bypassing the site and completing the transaction directly.

In your case, neither you nor the hotel is trying to pull anything underhanded. However, it all looks the same from the viewpoint of the website. You found a room on the site, and now you want to book that room directly with the hotel and bypass the site. If the hotel goes along with it and get caught, they risk getting kicked off of the website completely. Given the amount of business they get through that site, it’s too big of a risk for them. Ask the front desk if you can borrow the computer in their business center, and use it to book the room on the site.

I don’t know if this applies to booking.com, but in some cases a company may have a corporate relationship with a hotel which means that they are always entitled to the lowest offered rate or better.
i.e. If anyone else gets a price better than their negotiated corporate rate they can also have rooms at that price.

In these circumstances the hotels will offer spare rooms via web brokers as “mystery hotels” where the name of the hotel isn’t mentioned in the listing, but it’s very easy to work out which one it actually is with a bit of digging.
This gets around the problem associated with the corporate rate as it’s not being directly offered.

If you pay less, you get less. Rooms booked through a consolidator come from a different pool than rooms booked directly through the hotel (by phone, on website, or in person). The rooms may be larger, have better amenities, be cleaned by more experienced staff, etc. You won’t earn any loyalty rewards points by booking through a consolidator. If you have any special requests — such as booking multiple rooms near each other, early checkout, late check-in — the hotel will be much more likely to accommodate you if you book through the hotel, but won’t have any motivation to do so if you book through a consolidator.

In addition, selling rooms through multiple channels allows the hotel to perform market segmentation. People who are bargain sensitive will book through the consolidator and endure the annoyances, similar to booking “basic economy” vs “economy” vs “premium economy” on an airline.

The same way why you like shopping online and not dragging yourself all the way to a few stores to get the few things you want. It’s more convenient.

Business owners are focusing on developing their customer relations online, and not on-site. In the early time, you actually could ask for a discount, they will ask you to wait and then they call some sort of a manager, who comes with a big smile and use some human-to-human marketing techniques, then gives you a little discount and makes you go to your room feeling like a king.

All of this has shifted to online resources, where booking.com or other online merchants will do the job for them, and little by little the actual businesses started to lose the technique of making offers..

You were the “customer” to the hotel, now the hotel itself is a customer to the booking.com and other online merchants. They are paying fees to use their services, these fees are paid so booking.com can do these things for them.

Aren’t the fully automated hotels available now? you book, check-in and check-out online with no human interactions! Just wait for it and most of them will be the same. What you have been through is just the end of a transition period where the left-over humans who are supposed to do the job lost it to the digital ones.

I’d expect this to happen to chain hotels where, as you guessed, the front desk has zero price matching powers. And the chain already allocated those rooms to booking.com — it’s even possible you can’t get a room from the front desk even though booking.com has them. Insanity or not, this industry is very inflexible. Also, I’d think the main reason is bookkeeping // accounting // card handling — consider how easy it is for them when dealing with booking.com, it’s essentially “here’s a bank wire for all the rooms we sold this month” (possibly it’s not for the single property but per corporate parent!) versus “here is a credit card which might or might not be stolen for my single night stay”.