Molecular catch bonds are ubiquitous in biology and essential for processes like leucocyte extravasion¹ and cellular mechanosensing². Unlike normal (slip) bonds, catch bonds strengthen under tension. The current paradigm is that this feature provides ‘strength on demand³’, thus enabling cells to increase rigidity under stress^1,4–6. However, catch bonds are often weaker than slip bonds because they have cryptic binding sites that are usually buried^7,8. Here we show that catch bonds render reconstituted cytoskeletal actin networks stronger than slip bonds, even though the individual bonds are weaker. Simulations show that slip bonds remain trapped in stress-free areas, whereas weak binding allows catch bonds to mitigate crack initiation by moving to high-tension areas. This ‘dissociation on demand’ explains how cells combine mechanical strength with the adaptability required for shape change, and is relevant to diseases where catch bonding is compromised^7,9, including focal segmental glomerulosclerosis¹⁰ caused by the α-actinin-4 mutant studied here. We surmise that catch bonds are the key to create life-like materials.