If a photon truly goes through both slits (at the same time), then why can't we detect it at both slits (at the same time)?

Think of it this way: A photon is the detection event. When there is only one photon, there is only one detection event. The probability distribution of detection events is associated with the photon's wavefunction.

If the photon truly goes through both slits (at the same time), then why can't we detect it at both slits (at the same time)?

Alright, let's play some word games:

This isn't a well-defined question. "Detect a particle" doesn't mean anything in quantum mechanics. Quantum mechanical measurements are always measurements of specific observables. There is no holistic act of "observing all properties of a system at once" like there is in classical mechanics - a measurement is always specific to the one observable it measures, and the measurement irrevocably alters the state of the system being measured.

People often use "detect a particle" as shorthand for "perform a position measurement of a particle". By definition, a measurement of position has as its outcome a single position, and interacts with the state of the particle being measured such that it now really is in the state in which it is at that single position and nowhere else. So if you could perform position measurements that yielded both slits as the position of the particle, this would mean you have performed an impossible feat - there are now two particles, each in the state of being at one slit and that slit only. Quantum mechanics may be weird, but it is hopefully clear it is not this weird - we cannot duplicate a particle out of thin air just by measuring it.

If you don't insist on "detect" meaning "performing a position measurement", then of course the standard double slit setup is a "detection" of the photon at both slits - the pattern on the screen is only explainable by the particle's wavefunction passing through both slits and interfering with itself. This is of course just indirect reasoning - there simply is no observable whose eigenstates would naively correspond to "we have detected the photon at both slits at once".

Lastly, you seem to confuse "interacting" with "measuring" or "detecting". Of course we can interact with the particle at both slits - we just cannot perform position measurements (or other "which-way" measurements) at both slits and expect them to yield the impossible result of the particle split in two. But if you look at more sophisticated setups like the quantum erasers, there certainly is interaction with the particle at both slits - just carefully set up to not destroy the interference pattern, and hence no obtaining useable which-way information.

We've had a lot of answers already (because this problem invites them), but let me offer one more way to think about it. (As best I can tell, this is the interpretation of quantum mechanics closest to the point I'll make. As @PedroA notes below, what follows is interpretation-dependent.)

If the photon truly goes through both slits (at the same time), then why can't we detect it at both slits (at the same time)?

I think you're imagining we, as the scientists with our detector, are a classical system studying a separate quantum-mechanical one. But the entire experiment, including the detector and whoever inspects it, is also part of the quantum-mechanical setup. Our superposition isn't just of the photon passing through slit $1$ and its passing through slit $2$; it's of us detecting one and us detecting the other.

From a God's-eye point of view (if there is such a thing), we are superposed between announcing one result and announcing the other. We're not outside a quantum-mechanical system with such a God's-eye view, and therefore don't see the whole of the superposition. Hence we only see one result, not a bit of both.